Manifold Matching Complexes
Combinatorics
2020-03-24 v3
Abstract
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 sphere or balls.
Keywords
Cite
@article{arxiv.1906.03328,
title = {Manifold Matching Complexes},
author = {Margaret Bayer and Bennet Goeckner and Marija Jelić Milutinović},
journal= {arXiv preprint arXiv:1906.03328},
year = {2020}
}
Comments
43 pages, 32 figures Version 2 added a reference. Version 2 extends the theorems by weakening the hypotheses from combinatorial to homology manifolds, but shows the manifolds that occur are all combinatorial