SimplifiedComplex(K):: RegularCWComplex --> RegularCWComplex
SimplifiedComplex(K):: PurePermComplex --> PurePermComplex
SimplifiedComplex(R):: FreeResolution --> FreeResolution
SimplifiedComplex(C):: ChainComplex --> ChainComplex

Inputs a regular CW-complex or a pure permutahedral complex K and returns a homeomorphic complex with possibly fewer cells and certainly no more cells.

Inputs a free \mathbb ZG-resolution R of \mathbb Z and returns a \mathbb ZG-resolution S with potentially fewer free generators.

Inputs a chain complex C of free abelian groups and returns a chain homotopic chain complex D with potentially fewer free generators.