Topology Seminar - "Groups acting on contractible complexes with a strict fundamental doman", Dr Nansen Petrosyan (Southampton) Seminar

Event details

There are many examples of groups that act on contractible simplicial complexes with a strict fundamental domain, e.g. free products with amalgamation, graph products of groups or more generally groups acting chamber transitively on buildings. In this talk, primary examples will be finitely generated Coxeter groups acting on associated Davis complex. We will discuss a construction that replaces the Davis complex with a “simpler" complex called the Bestvina complex. This complex will have the smallest possible dimension equal to the virtual cohomological dimension of the group and will be equivariantly homotopy equivalent to the Davis complex. This will allow us to compute the Bredon cohomological dimension of the group with respect to the family of finite subgroups. I will give examples of the Bestvina complex and discuss some applications and generalisations. One such application is that if a group acts on a contractible complex X with a strict fundamental domain and also has Bredon cohomological dimension at most one for the family of stabiliser subgroups, then X equivariantly deformation retracts onto a tree.