Bestvina's normal form complex and the homology of Garside groups.
type: Item
instance of: scholarly article
title: Bestvina's normal form complex and the homology of Garside groups.
zbMATH Open document ID: 1064.20044
DOI: 10.1023/B:GEOM.0000024696.69357.73
author: Ruth Charney
author: John Meier
author: Kim Whittlesey
published in: Geometriae Dedicata
publication date: 2004-08-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0202228
review text: A Garside group is a group admitting a finite lattice generating set \(\mathcal D\). Using techniques developed by Bestvina for Artin groups of finite type, the authors 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 \(\mathcal D\), 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 nonpositive curvature condition. Under a certain tameness condition, this implies that every solvable subgroup of \(G\) is virtually Abelian.
reviewed by: Mina Teicher
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 2083429
zbMATH Keywords: Artin groups
zbMATH Keywords: duality groups
zbMATH Keywords: Garside groups
MaRDI profile type: Publication
arXiv ID: math/0202228
OpenAlex ID: W2011897026
Recommended article: Bestvina complex for group actions with a strict fundamental domain
Recommended article: The cohomology of Bestvina-Brady groups.
Recommended article: Homotopical and combinatorial aspects of the theory of normal series in groups.
Recommended article: Homology of Gaussian groups.
Recommended article: Homologie des groupes et généralisations du théorème de Borsuk–Ulam
Recommended article: Simplicial structures and normal forms for mapping class groups and braid groups
Recommended article: Q6039747
Recommended article: On certain homological invariants of groups.
Recommended article: Q3800257
Recommended article: Complex cobordism and formal groups
description: scientific article