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[]  \T1/cmtt/m/n/10.95 RestrictedEquivariantCWComplex(Y,H):: RegCWComplex, Grou
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[]\T1/ptm/m/n/10.95 Reads an im-age file iden-ti-fied by a string str such as "
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[]  \T1/cmtt/m/n/10.95 ReadImageAsFilteredPureCubicalComplex(str,n):: String, I
nt --> FilteredPureCubicalComplex 
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[]  \T1/cmtt/m/n/10.95 ReadPDBfileAsPurePermutahedralComplex(str,r):: String, I
nt --> PurePermComplex 
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[]  \T1/cmtt/m/n/10.95 ConcentricFiltration(K,n):: PureCubicalComplex, Int --> 
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[]  \T1/cmtt/m/n/10.95 DirectProduct(M,N):: PureCubicalComplex, PureCubicalComp
lex --> PureCubicalComplex 
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[]  \T1/cmtt/m/n/10.95 ThickeningFiltration(K,n):: PureCubicalComplex, Int --> 
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[]  \T1/cmtt/m/n/10.95 ThickeningFiltration(K,n,s):: PureCubicalComplex, Int, I
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[]  \T1/cmtt/m/n/10.95 ContractedComplex(K,S):: PureCubicalComplex, PureCubical
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[]  \T1/cmtt/m/n/10.95 ContractedComplex(K):: FilteredPureCubicalComplex --> Fi
lteredPureCubicalComplex 
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[]  \T1/cmtt/m/n/10.95 ContractedComplex(K,S):: PurePermComplex, PurePermComple
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[]  \T1/cmtt/m/n/10.95 PureComplexDifference(M,N):: PureCubicalComplex, PureCub
icalComplex --> PureCubicalComplex 
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[]  \T1/cmtt/m/n/10.95 PureComplexDifference(M,N):: PurePermComplex, PurePermCo
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[]  \T1/cmtt/m/n/10.95 PureComplexInterstection(M,N):: PureCubicalComplex, Pure
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[]  \T1/cmtt/m/n/10.95 PureComplexIntersection(M,N):: PurePermComplex, PurePerm
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[]  \T1/cmtt/m/n/10.95 PureComplexUnion(M,N):: PureCubicalComplex, PureCubicalC
omplex --> PureCubicalComplex 
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[]  \T1/cmtt/m/n/10.95 ZigZagContractedComplex(K):: FilteredPureCubicalComplex 
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[]  \T1/cmtt/m/n/10.95 PersistentBettiNumbers(K,n,p):: FilteredPureCubicalCompl
ex, Int, Int --> List 
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[]  \T1/cmtt/m/n/10.95 PersistentBettiNumbers(K,n,p):: FilteredSparseChainCompl
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[]  \T1/cmtt/m/n/10.95 ChainMap(X,A,Y,B):: PureCubicalComplex, PureCubicalCompl
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[]  \T1/cmtt/m/n/10.95 FilteredTensorWithIntegersModP(R,p):: FreeResolution, In
t --> FilteredChainComplex 
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[29]
Chapter 2.

Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
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! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1723 \begin{verbatim}
                         EquivariantChainMap(R,S,f):: FreeResolution, FreeRe...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1723 \begin{verbatim}
                         EquivariantChainMap(R,S,f):: FreeResolution, FreeRe...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1723 \begin{verbatim}
                         EquivariantChainMap(R,S,f):: FreeResolution, FreeRe...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.1723 \begin{verbatim}
                         EquivariantChainMap(R,S,f):: FreeResolution, FreeRe...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1723 \begin{verbatim}
                         EquivariantChainMap(R,S,f):: FreeResolution, FreeRe...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1723 \begin{verbatim}
                         EquivariantChainMap(R,S,f):: FreeResolution, FreeRe...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
l.1723 \begin{verbatim}
                         EquivariantChainMap(R,S,f):: FreeResolution, FreeRe...
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
l.1723 \begin{verbatim}
                         EquivariantChainMap(R,S,f):: FreeResolution, FreeRe...
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.


Overfull \hbox (111.86661pt too wide) in paragraph at lines 1724--1724
[]  \T1/cmtt/m/n/10.95 EquivariantChainMap(R,S,f):: FreeResolution, FreeResolut
ion, GroupHomomorphisms --> EquiChainMap 
 []


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1724 \end{verbatim}
                     
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: \begin{tabular} on input line 1722 ended by \end{verbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1724 \end{verbatim}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.1724 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted.
<inserted text> 
                $
l.1724 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1724 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

[30

]
! Misplaced \crcr.
\endtabular ->\crcr 
                    \egroup \egroup $\egroup 
l.1823 \end{tabular}
                    \\[2mm]
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup 
                            \egroup $\egroup 
l.1823 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup \egroup 
                                    $\egroup 
l.1823 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.1823 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{center} on input line 1721 ended by \end{tabular}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1823 \end{tabular}
                    \\[2mm]
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.1823 \end{tabular}
                    \\[2mm]
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.


Underfull \hbox (badness 10000) in paragraph at lines 1823--1824

 []


! LaTeX Error: \begin{document} ended by \end{center}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1824 \end{center}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.1824 \end{center}
                   
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.1824 \end{center}
                   
Things are pretty mixed up, but I think the worst is over.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1828 \begin{verbatim}
                         LeibnizComplex(g,n):: LeibnizAlgebra, Int --> Chain...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1828 \begin{verbatim}
                         LeibnizComplex(g,n):: LeibnizAlgebra, Int --> Chain...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1828 \begin{verbatim}
                         LeibnizComplex(g,n):: LeibnizAlgebra, Int --> Chain...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.1828 \begin{verbatim}
                         LeibnizComplex(g,n):: LeibnizAlgebra, Int --> Chain...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1828 \begin{verbatim}
                         LeibnizComplex(g,n):: LeibnizAlgebra, Int --> Chain...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1828 \begin{verbatim}
                         LeibnizComplex(g,n):: LeibnizAlgebra, Int --> Chain...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
l.1828 \begin{verbatim}
                         LeibnizComplex(g,n):: LeibnizAlgebra, Int --> Chain...
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
l.1828 \begin{verbatim}
                         LeibnizComplex(g,n):: LeibnizAlgebra, Int --> Chain...
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1829 \end{verbatim}
                     
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: \begin{tabular} on input line 1827 ended by \end{verbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1829 \end{verbatim}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.1829 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted.
<inserted text> 
                $
l.1829 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1829 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Misplaced \crcr.
\endtabular ->\crcr 
                    \egroup \egroup $\egroup 
l.1833 \end{tabular}
                    \\[2mm]
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup 
                            \egroup $\egroup 
l.1833 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup \egroup 
                                    $\egroup 
l.1833 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.1833 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{center} on input line 1826 ended by \end{tabular}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1833 \end{tabular}
                    \\[2mm]
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.1833 \end{tabular}
                    \\[2mm]
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.


Underfull \hbox (badness 10000) in paragraph at lines 1833--1834

 []


! LaTeX Error: \begin{document} ended by \end{center}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1834 \end{center}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.1834 \end{center}
                   
Things are pretty mixed up, but I think the worst is over.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1838 \begin{verbatim}
                         HomToIntegers(C):: ChainComplex --> CochainComplex
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1838 \begin{verbatim}
                         HomToIntegers(C):: ChainComplex --> CochainComplex
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1838 \begin{verbatim}
                         HomToIntegers(C):: ChainComplex --> CochainComplex
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.1838 \begin{verbatim}
                         HomToIntegers(C):: ChainComplex --> CochainComplex
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1838 \begin{verbatim}
                         HomToIntegers(C):: ChainComplex --> CochainComplex
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1838 \begin{verbatim}
                         HomToIntegers(C):: ChainComplex --> CochainComplex
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
l.1838 \begin{verbatim}
                         HomToIntegers(C):: ChainComplex --> CochainComplex
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
l.1838 \begin{verbatim}
                         HomToIntegers(C):: ChainComplex --> CochainComplex
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1839 \end{verbatim}
                     
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: \begin{tabular} on input line 1837 ended by \end{verbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1839 \end{verbatim}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.1839 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted.
<inserted text> 
                $
l.1839 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1839 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

[31]
Overfull \hbox (15.6743pt too wide) in paragraph at lines 1857--1857
[]  \T1/cmtt/m/n/10.95 HomToIntegralModule(R,A):: FreeResolution, GroupHomomorp
hism --> CochainComplex 
 []

! Misplaced \crcr.
\endtabular ->\crcr 
                    \egroup \egroup $\egroup 
l.1896 \end{tabular}
                    \\[2mm]
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup 
                            \egroup $\egroup 
l.1896 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup \egroup 
                                    $\egroup 
l.1896 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.1896 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{center} on input line 1836 ended by \end{tabular}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1896 \end{tabular}
                    \\[2mm]
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.1896 \end{tabular}
                    \\[2mm]
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.


Underfull \hbox (badness 10000) in paragraph at lines 1896--1897

 []


! LaTeX Error: \begin{document} ended by \end{center}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1897 \end{center}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.1897 \end{center}
                   
Things are pretty mixed up, but I think the worst is over.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1901 \begin{verbatim}
                         AreIsomorphicGradedAlgebras(A,B):: PresentedGradedA...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1901 \begin{verbatim}
                         AreIsomorphicGradedAlgebras(A,B):: PresentedGradedA...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1901 \begin{verbatim}
                         AreIsomorphicGradedAlgebras(A,B):: PresentedGradedA...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.1901 \begin{verbatim}
                         AreIsomorphicGradedAlgebras(A,B):: PresentedGradedA...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1901 \begin{verbatim}
                         AreIsomorphicGradedAlgebras(A,B):: PresentedGradedA...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1901 \begin{verbatim}
                         AreIsomorphicGradedAlgebras(A,B):: PresentedGradedA...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
l.1901 \begin{verbatim}
                         AreIsomorphicGradedAlgebras(A,B):: PresentedGradedA...
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
l.1901 \begin{verbatim}
                         AreIsomorphicGradedAlgebras(A,B):: PresentedGradedA...
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.


Overfull \hbox (94.8915pt too wide) in paragraph at lines 1902--1902
[]  \T1/cmtt/m/n/10.95 AreIsomorphicGradedAlgebras(A,B):: PresentedGradedAlgebr
a, PresentedGradedAlgebra --> Boolean 
 []


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1902 \end{verbatim}
                     
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: \begin{tabular} on input line 1900 ended by \end{verbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1902 \end{verbatim}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.1902 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted.
<inserted text> 
                $
l.1902 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1902 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

[32] [33]
! Misplaced \crcr.
\endtabular ->\crcr 
                    \egroup \egroup $\egroup 
l.1993 \end{tabular}
                    \\[2mm]
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup 
                            \egroup $\egroup 
l.1993 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup \egroup 
                                    $\egroup 
l.1993 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.1993 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{center} on input line 1899 ended by \end{tabular}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1993 \end{tabular}
                    \\[2mm]
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.1993 \end{tabular}
                    \\[2mm]
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.


Underfull \hbox (badness 10000) in paragraph at lines 1993--1994

 []


! LaTeX Error: \begin{document} ended by \end{center}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1994 \end{center}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.1994 \end{center}
                   
Things are pretty mixed up, but I think the worst is over.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1998 \begin{verbatim}
                         GroupCohomology(G,k):: Group, Int --> List
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1998 \begin{verbatim}
                         GroupCohomology(G,k):: Group, Int --> List
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1998 \begin{verbatim}
                         GroupCohomology(G,k):: Group, Int --> List
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.1998 \begin{verbatim}
                         GroupCohomology(G,k):: Group, Int --> List
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1998 \begin{verbatim}
                         GroupCohomology(G,k):: Group, Int --> List
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1998 \begin{verbatim}
                         GroupCohomology(G,k):: Group, Int --> List
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
l.1998 \begin{verbatim}
                         GroupCohomology(G,k):: Group, Int --> List
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
l.1998 \begin{verbatim}
                         GroupCohomology(G,k):: Group, Int --> List
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1999 \end{verbatim}
                     
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: \begin{tabular} on input line 1997 ended by \end{verbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1999 \end{verbatim}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.1999 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted.
<inserted text> 
                $
l.1999 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.1999 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

[34]
Overfull \hbox (21.33267pt too wide) in paragraph at lines 2031--2031
[]  \T1/cmtt/m/n/10.95 PrimePartDerivedFunctor(G,R,A,k):: Group, FreeResolution
, Function, Int --> List 
 []

[35]
! Missing } inserted.
<inserted text> 
                }
l.2078 ...ite abelian $p$-group $H_n{G,\mathbb Z)$
                                                  . \\
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Misplaced \crcr.
\endtabular ->\crcr 
                    \egroup \egroup $\egroup 
l.2079 \end{tabular}
                    \\[2mm]
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup 
                            \egroup $\egroup 
l.2079 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup \egroup 
                                    $\egroup 
l.2079 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.2079 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{center} on input line 1996 ended by \end{tabular}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2079 \end{tabular}
                    \\[2mm]
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.2079 \end{tabular}
                    \\[2mm]
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.


Underfull \hbox (badness 10000) in paragraph at lines 2079--2080

 []


! LaTeX Error: \begin{document} ended by \end{center}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2080 \end{center}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.2080 \end{center}
                   
Things are pretty mixed up, but I think the worst is over.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2084 \begin{verbatim}
                         GroupAlgebraAsFpGModule:: Group --> FpGModule
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2084 \begin{verbatim}
                         GroupAlgebraAsFpGModule:: Group --> FpGModule
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2084 \begin{verbatim}
                         GroupAlgebraAsFpGModule:: Group --> FpGModule
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.2084 \begin{verbatim}
                         GroupAlgebraAsFpGModule:: Group --> FpGModule
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2084 \begin{verbatim}
                         GroupAlgebraAsFpGModule:: Group --> FpGModule
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2084 \begin{verbatim}
                         GroupAlgebraAsFpGModule:: Group --> FpGModule
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
l.2084 \begin{verbatim}
                         GroupAlgebraAsFpGModule:: Group --> FpGModule
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
l.2084 \begin{verbatim}
                         GroupAlgebraAsFpGModule:: Group --> FpGModule
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2085 \end{verbatim}
                     
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: \begin{tabular} on input line 2083 ended by \end{verbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2085 \end{verbatim}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.2085 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted.
<inserted text> 
                $
l.2085 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2085 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Misplaced \crcr.
\endtabular ->\crcr 
                    \egroup \egroup $\egroup 
l.2112 \end{tabular}
                    \\[2mm]
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup 
                            \egroup $\egroup 
l.2112 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup \egroup 
                                    $\egroup 
l.2112 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.2112 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{center} on input line 2082 ended by \end{tabular}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2112 \end{tabular}
                    \\[2mm]
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.2112 \end{tabular}
                    \\[2mm]
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.


Underfull \hbox (badness 10000) in paragraph at lines 2112--2113

 []


! LaTeX Error: \begin{document} ended by \end{center}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2113 \end{center}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.2113 \end{center}
                   
Things are pretty mixed up, but I think the worst is over.

! Too many }'s.
l.2115  }
         
You've closed more groups than you opened.
Such booboos are generally harmless, so keep going.

[36]
Chapter 3.

! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2123 \begin{verbatim}
                         CcGroup(N,f):: GOuterGroup, StandardCocycle --> CcG...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2123 \begin{verbatim}
                         CcGroup(N,f):: GOuterGroup, StandardCocycle --> CcG...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2123 \begin{verbatim}
                         CcGroup(N,f):: GOuterGroup, StandardCocycle --> CcG...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.2123 \begin{verbatim}
                         CcGroup(N,f):: GOuterGroup, StandardCocycle --> CcG...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2123 \begin{verbatim}
                         CcGroup(N,f):: GOuterGroup, StandardCocycle --> CcG...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2123 \begin{verbatim}
                         CcGroup(N,f):: GOuterGroup, StandardCocycle --> CcG...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
l.2123 \begin{verbatim}
                         CcGroup(N,f):: GOuterGroup, StandardCocycle --> CcG...
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
l.2123 \begin{verbatim}
                         CcGroup(N,f):: GOuterGroup, StandardCocycle --> CcG...
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2124 \end{verbatim}
                     
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: \begin{tabular} on input line 2122 ended by \end{verbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2124 \end{verbatim}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.2124 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted.
<inserted text> 
                $
l.2124 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2124 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Misplaced \crcr.
\endtabular ->\crcr 
                    \egroup \egroup $\egroup 
l.2146 \end{tabular}
                    \\[2mm]
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup 
                            \egroup $\egroup 
l.2146 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup \egroup 
                                    $\egroup 
l.2146 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.2146 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{center} on input line 2121 ended by \end{tabular}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2146 \end{tabular}
                    \\[2mm]
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.2146 \end{tabular}
                    \\[2mm]
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.


Underfull \hbox (badness 10000) in paragraph at lines 2146--2147

 []


! LaTeX Error: \begin{document} ended by \end{center}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2147 \end{center}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.2147 \end{center}
                   
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.2147 \end{center}
                   
Things are pretty mixed up, but I think the worst is over.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2151 \begin{verbatim}
                         ActedGroup(M):: GOuterGroup --> Group
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2151 \begin{verbatim}
                         ActedGroup(M):: GOuterGroup --> Group
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2151 \begin{verbatim}
                         ActedGroup(M):: GOuterGroup --> Group
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.2151 \begin{verbatim}
                         ActedGroup(M):: GOuterGroup --> Group
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2151 \begin{verbatim}
                         ActedGroup(M):: GOuterGroup --> Group
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2151 \begin{verbatim}
                         ActedGroup(M):: GOuterGroup --> Group
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
l.2151 \begin{verbatim}
                         ActedGroup(M):: GOuterGroup --> Group
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
l.2151 \begin{verbatim}
                         ActedGroup(M):: GOuterGroup --> Group
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2152 \end{verbatim}
                     
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: \begin{tabular} on input line 2150 ended by \end{verbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2152 \end{verbatim}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.2152 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted.
<inserted text> 
                $
l.2152 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2152 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

[37

]
! Misplaced \crcr.
\endtabular ->\crcr 
                    \egroup \egroup $\egroup 
l.2188 \end{tabular}
                    \\[2mm]
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup 
                            \egroup $\egroup 
l.2188 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup \egroup 
                                    $\egroup 
l.2188 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.2188 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{center} on input line 2149 ended by \end{tabular}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2188 \end{tabular}
                    \\[2mm]
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.2188 \end{tabular}
                    \\[2mm]
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.


Underfull \hbox (badness 10000) in paragraph at lines 2188--2189

 []


! LaTeX Error: \begin{document} ended by \end{center}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2189 \end{center}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.2189 \end{center}
                   
Things are pretty mixed up, but I think the worst is over.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2193 \begin{verbatim}
                         CohomologyModule(C,n):: GCocomplex, Int --> GOuterG...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2193 \begin{verbatim}
                         CohomologyModule(C,n):: GCocomplex, Int --> GOuterG...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2193 \begin{verbatim}
                         CohomologyModule(C,n):: GCocomplex, Int --> GOuterG...

Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.2193 \begin{verbatim}
                         CohomologyModule(C,n):: GCocomplex, Int --> GOuterG...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2193 \begin{verbatim}
                         CohomologyModule(C,n):: GCocomplex, Int --> GOuterG...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2193 \begin{verbatim}
                         CohomologyModule(C,n):: GCocomplex, Int --> GOuterG...
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
l.2193 \begin{verbatim}
                         CohomologyModule(C,n):: GCocomplex, Int --> GOuterG...
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
l.2193 \begin{verbatim}
                         CohomologyModule(C,n):: GCocomplex, Int --> GOuterG...
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.


! LaTeX Error: Something's wrong--perhaps a missing \item.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2194 \end{verbatim}
                     
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.


! LaTeX Error: \begin{tabular} on input line 2192 ended by \end{verbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2194 \end{verbatim}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing } inserted.
<inserted text> 
                }
l.2194 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted.
<inserted text> 
                $
l.2194 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.2194 \end{verbatim}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Misplaced \crcr.
\endtabular ->\crcr 
                    \egroup \egroup $\egroup 
l.2208 \end{tabular}
                    \\[2mm]
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup 
                            \egroup $\egroup 
l.2208 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten \endgroup.
\endtabular ->\crcr \egroup \egroup 
                                    $\egroup 
l.2208 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.2208 \end{tabular}
                    \\[2mm]
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{center} on input line 2191 ended by \end{tabular}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2208 \end{tabular}
                    \\[2mm]
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.2208 \end{tabular}
                    \\[2mm]
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.


Underfull \hbox (badness 10000) in paragraph at lines 2208--2209

 []


! LaTeX Error: \begin{document} ended by \end{center}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2209 \end{center}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.2209 \end{center}
                   
Things are pretty mixed up, but I think the worst is over.

! Too many }'s.
l.2211  }
         
You've closed more groups than you opened.
Such booboos are generally harmless, so keep going.

[38]
Chapter 4.

! LaTeX Error: There's no line here to end.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2218  \\
          
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


! LaTeX Error: There's no line here to end.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2219  \\
          
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


! LaTeX Error: There's no line here to end.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.2220  \index
              {TietzeReducedResolution}::::::::::::::::::::::::\\
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


Underfull \hbox (badness 10000) in paragraph at lines 2220--2222

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[39

]
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LaTeX Warning: Command \textperiodcentered invalid in math mode on input line 2
308.

LaTeX Font Info:    Try loading font information for TS1+ptm on input line 2308
.
(/usr/share/texmf-texlive/tex/latex/psnfss/ts1ptm.fd
File: ts1ptm.fd 2001/06/04 font definitions for TS1/ptm.
)

LaTeX Warning: Command \textperiodcentered invalid in math mode on input line 2
308.


LaTeX Warning: Command \textperiodcentered invalid in math mode on input line 2
308.


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308.


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308.

Missing character: There is no · in font zptmcm7t!
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[40]
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[]\T1/ptm/m/n/10.95 In ad-di-tion to the usual com-po-nents, the res-o-lu-tion 
$\OML/ztmcm/m/it/10.95 R$ \T1/ptm/m/n/10.95 has the com-po-nent
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[]\T1/ptm/m/n/10.95 This func-tion can be ap-plied to in-fi-nite groups $\OML/z
tmcm/m/it/10.95 G$\T1/ptm/m/n/10.95 . For fi-nite groups the func-tion
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[]\T1/ptm/m/n/10.95 If $\OML/ztmcm/m/it/10.95 G$ \T1/ptm/m/n/10.95 is fi-nite t
hen the func-tion $\OML/ztmcm/m/it/10.95 ResolutionFiniteSubgroup\OT1/ztmcm/m/n
/10.95 (\OML/ztmcm/m/it/10.95 R; G; K\OT1/ztmcm/m/n/10.95 )$ \T1/ptm/m/n/10.95 
will prob-a-bly work
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[47]
Chapter 5.

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[48

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Chapter 6.

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[49

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Chapter 7.

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\T1/ptm/m/n/10.95 a res-o-lu-tion can be pro-duced us-ing TwisterTen-sor-Prod-u
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[53]
Chapter 8.

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[56]
Chapter 9.

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[59]
Chapter 10.

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Chapter 11.

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Chapter 12.

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[72]
Chapter 13.

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Chapter 14.

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[]\T1/ptm/m/n/10.95 For non-nilpotent groups the im-ple-men-ta-tion of the func
-tion
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[79]
Chapter 15.

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\OML/ztmcm/m/it/10.95 E:homomorphism$ \T1/ptm/m/n/10.95 is a Lie ho-mo-mor-phis
m $\OML/ztmcm/m/it/10.95 ^^V \OT1/ztmcm/m/n/10.95 : (\OML/ztmcm/m/it/10.95 L \O
MS/ztmcm/m/n/10.95 ^ \OML/ztmcm/m/it/10.95 L\OT1/ztmcm/m/n/10.95 ) [][]\OMS/ztm
cm/m/n/10.95 ! \OML/ztmcm/m/it/10.95 L$ \T1/ptm/m/n/10.95 from the non-abelian 
ex-te-rior
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Chapter 16.

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Chapter 17.

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\T1/ptm/m/n/10.95 "SL(2,O-2)" , "SL(2,O-7)" , "SL(2,O-11)" , "SL(2,O-19)" , "SL
(2,O-43)" , "SL(2,O-67)" ,
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Chapter 18.

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Chapter 19.

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Chapter 20.

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Chapter 21.

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Chapter 22.

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[100]
Chapter 23.

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[102]
Chapter 24.

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\T1/ptm/m/n/10.95 This func-tion ap-plies both to cat-1-groups for which IsHap-
Ca-tOne-Group(G) is true, and to
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[]\T1/ptm/m/n/10.95 This func-tion in-puts a free $\OML/ztmcm/m/it/10.95 ZG$\T1
/ptm/m/n/10.95 -resolution $\OML/ztmcm/m/it/10.95 R$\T1/ptm/m/n/10.95 . It firs
t con-structs the chain com-plex
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[107]
Chapter 25.

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Chapter 26.

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Chapter 27.

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Chapter 28.

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Chapter 32.

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Chapter 33.

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[137] [138]
Chapter 34.

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Chapter 35.

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Chapter 37.

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