On the homotopy type of the matching complex of small size

2020/02/10 Mon 17:15 - 18:15
Room 609, Building No.6
Shuichi Tsukuda
University of Ryukyus

The matching complex $M_n$ is a simplicial complex whose vertices are two element subset of $[n]=\{1,\ldots,n\}$ and faces are matchings on $[n]$. The topological properties of the matching complex were first studied by Bouc to study the Quillen complex at the prime 2 of the symmetric group. The rational homology of the matching complex is determined by Bouc and it is known that there are many torsions in integral homology. In this talk, I will discuss the homotopy type of the matching complex for small $n$.