Abstract:

Forman's discrete Morse theory (DMT) is a much used tool to calculate the homotopy type of simplicial complexes of combinatorial interest. Many such complexes are naturally equipped with some group action. I will show how a mild generalization of DMT can be used to calculate the G-homotopy type of a simplicial complex, acted upon by a group G. I will illustrate the theory by determining certain G-invariants for the complex of non-connected graphs, with a particular group G acting on it.