Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products.
type: Item
instance of: scholarly article
title: Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products.
zbMATH Open document ID: 1281.20062
DOI: 10.4171/GGD/164
author: Michael W. Davis
author: Boris Okun
published in: Groups, Geometry, and Dynamics
publication date: 2012-10-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/1002.2564
review text: Summary: We compute: \(\bullet\) the cohomology with group ring coefficients of Artin groups (or actually, of their associated Salvetti complexes), of Bestvina-Brady groups of type FP, and of graph products of groups, \(\bullet\) the \(L^2\)-Betti numbers of Bestvina-Brady groups of type FP over \(\mathbb Q\), and of graph products of groups, \(\bullet\) the weighted \(L^2\)-Betti numbers of graph products of Coxeter groups. -- In the case of arbitrary graph products there is an additional proviso: either all factors are infinite or all are finite.
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20E06
zbMATH DE Number: 6088869
zbMATH Keywords: cohomology
zbMATH Keywords: Artin groups
zbMATH Keywords: Bestvina-Brady groups
zbMATH Keywords: buildings
zbMATH Keywords: Coxeter groups
zbMATH Keywords: graph products
zbMATH Keywords: right-angled Artin group
zbMATH Keywords: \(L^2\)-Betti numbers
zbMATH Keywords: weighted \(L^2\)-cohomology
MaRDI profile type: Publication
arXiv ID: 1002.2564
cites work: Buildings
cites work: Decompositions of the polyhedral product functor with applications to moment-angle complexes and related spaces
cites work: Non-positively curved aspects of Artin groups of finite type
cites work: Morse theory and finiteness properties of groups
cites work: Connectivity at infinity for right angled Artin groups
cites work: Q3708977
cites work: Improper actions and higher connectivity at infinity
cites work: The K(π, 1)-Problem for Hyperplane Complements Associated to Infinite Reflection Groups
cites work: Q4266116
cites work: The cohomology of a Coxeter group with group ring coefficients
cites work: Q5431018
cites work: Examples of buildings constructed via covering spaces
cites work: Compactly supported cohomology of buildings.
cites work: Cohomology of Coxeter groups with group ring coefficients. II.
cites work: Weighted \(L^2\)-cohomology of Coxeter groups.
cites work: Right-angled Artin groups are commensurable with right-angled Coxeter groups
cites work: THE $\eltwo$-COHOMOLOGY OF ARTIN GROUPS
cites work: The topology at infinity of Coxeter groups and buildings
cites work: Vanishing theorems and conjectures for the 2-homology of right-angled Coxeter groups
cites work: Moment-angle complexes, monomial ideals and Massey products
cites work: Thin buildings.
cites work: Cohomology of buildings and of their automorphism groups.
cites work: Extensions of complexes of groups
cites work: Finite index subgroups of graph products.
cites work: Higher Generation Subgroup Sets and the Virtual Cohomological Dimension of Graph Products of Finite Groups
cites work: On linear and residual properties of graph products
cites work: Commensurability of graph products
cites work: The Cohomology of Right-Angled Artin Groups with Group Ring Coefficients
cites work: The cohomology of Bestvina-Brady groups.
cites work: Q3148984
cites work: The Homological Algebra of Artin Groups.
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description: scientific article; zbMATH DE number 6088869