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 GG-homotopy type of a simplicial complex. As an application, we determine the C2×Sn−2C2×Sn−2-homotopy type of the complex of non-connected graphs on nn nodes.