Cohomology computations for Artin groups, Bestvina–Brady groups, and graph products

Abstract

We compute: � the cohomology with group ring coefficients of Artin groups (or actually, of their asso- ciated Salvetti complexes), of Bestvina-Brady groups of type FP, and of graph products of groups, � the L 2 -Betti numbers of Bestvina-Brady groups of type FP over Q, and of graph products of groups, � the weighted L 2 -Betti numbers of graph products of Coxeter groups.