Bredon cohomological dimension for virtually abelian stabilisers for CAT(0) groups

Abstract

Given a discrete group [Formula: see text], for any integer [Formula: see text] we consider the family of all virtually abelian subgroups of [Formula: see text] of rank at most [Formula: see text]. We give an upper bound for the Bredon cohomological dimension of [Formula: see text] for this family for a certain class of groups acting on [Formula: see text] spaces. This covers the case of Coxeter groups, Right-angled Artin groups, fundamental groups of special cube complexes and graph products of finite groups. Our construction partially answers a question of Lafont.