Matching complexes of graphs

Abstract: The matching complex M(G) of a graph G is the simplicial complex with the vertex set given by edges of G and faces given by subsets of pairwise disjoint edges, i.e., matchings of G. There is a long history of the study of matching complexes, and there are many results on the topology of the matching complexes of interesting classes of graphs. We will discuss the reverse question: which simplicial complexes are matching complexes of graphs? In this talk we will answer this question for the homology manifolds, with and without boundary. While in dimension 2 there are several interesting manifolds, in dimension three and higher the only matching complexes are combinatorial spheres and combinatorial disks. Moreover, the graphs that produce manifold matching complexes are all constructed from the disjoint union of copies of a finite set of graphs. The talk is based on joint work with M. Bayer and B. Goeckner.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

Series comments: There is a mailing list for talk announcements. If you want to receive the announcements, send an e-mail to the organizer to subscribe to the mailing list.

The password for the zoom room is 123456