Bestvina's normal form complex and the homology of Garside groups

Abstract

A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(\pi,1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice D, and there is a simple sufficient condition that implies G is a duality group. The universal covers of these K(\pi,1)s enjoy Bestvina's weak non-positive curvature condition. Under a certain tameness condition, this implies that every solvable subgroup of G is virtually abelian.