ContractedComplex(K):: RegularCWComplex --> RegularCWComplex
ContractedComplex(K):: FilteredRegularCWComplex --> FilteredRegularCWComplex
ContractedComplex(K):: CubicalComplex --> CubicalComplex
ContractedComplex(K):: PureCubicalComplex --> PureCubicalComplex
ContractedComplex(K,S):: PureCubicalComplex, PureCubicalComplex --> PureCubicalComplex
ContractedComplex(K):: FilteredPureCubicalComplex --> FilteredPureCubicalComplex
ContractedComplex(K):: PurePermComplex --> PurePermComplex
ContractedComplex(K,S):: PurePermComplex, PurePermComplex --> PurePermComplex
ContractedComplex(K):: SimplicialComplex --> SimplicialComplex
ContractedComplex(G):: Graph --> Graph

Inputs a complex (regular CW, Filtered regular CW, pure cubical etc.) and returns a homotopy equivalent subcomplex.

Inputs a pure cubical complex or pure permutahedral complex K and a subcomplex S. It returns a homotopy equivalent subcomplex of K that contains S.

Inputs a graph G and returns a subgraph S such that the clique complexes of G and S are homotopy equivalent.