MANIFOLD MATCHING COMPLEXES
Margaret M. Bayer, Bennet Goeckner, Marija Jelić Milutinović · Mathematika · 2020
The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper, we completely characterize the pairs (graph, matching complex) for which the matching complex is a homology manifold, with or without boundary. Except in dimension two, all of these manifolds are spheres or balls.