Equivariant discrete Morse theory

In this paper, we study Forman’s discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain a theory that can be used to simplify the description of the G -homotopy type of a simplicial complex. As an application, we determine the C 2 × S n − 2 -homotopy type of the complex of non-connected graphs on n nodes.