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25 Regular CW-Spaces

25 Regular CW-Spaces

SimplicialComplexToRegularCWSpace(K)

Inputs a simplicial complex K and returns the corresponding regular CW-space.

CubicalComplexToRegularCWSpace(K)

Inputs a pure cubical complex (or cubical complex) K and returns the corresponding regular CW-space.

CriticalCellsOfRegularCWSpace(Y)

Inputs a regular CW-space Y and returns the critical cells of Y with respect to some discrete vector field. If Y does not initially have a discrete vector field then one is constructed.

ChainComplex(Y)

Inputs a regular CW-space Y and returns the cellular chain complex of a CW-space W whose cells correspond to the critical cells of Y with respect to some discrete vector field. If Y does not initially have a discrete vector field then one is constructed.

ChainComplexOfRegularCWSpace(Y)

Inputs a regular CW-space Y and returns the cellular chain complex of Y.

FundamentalGroup(Y) FundamentalGroup(Y,n)

Inputs a regular CW-space Y and, optionally, the number of some 0-cell. It returns the fundamental group of Y based at the 0-cell n. The group is returned as a finitely presented group. If n is not specified then it is set n=1. The algorithm requires a discrete vector field on Y. If Y does not initially have a discrete vector field then one is constructed.


 


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