On braid groups and right-angled Artin groups
type: Item
instance of: scholarly article
title: On braid groups and right-angled Artin groups
zbMATH Open document ID: 1302.55012
published in: Geometriae Dedicata
publication date: 2014-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0411368
review text: A \textit{right-angled Artin group} is a group with a presentation whose only relators are commutators between generators. A. Abrams and R. Ghrist conjectured in [\textit{A. Abrams}, Geom. Dedicata 92, 185--194 (2002; Zbl 1049.20023)] and [\textit{R. Ghrist}, AMS/IP Stud. Adv. Math. 24, 29--40 (2001; Zbl 1010.55012)] that braid groups of planar graphs are right-angled Artin groups. The authors prove that contractible graphs whose nodes (vertices of degree \(\geq 3\)) all lie in an interval (copy of \([0,1]\)) have right-angled braid groups.
reviewed by: Lee P. Neuwirth
Mathematics Subject Classification ID: 55R80
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 6358005
zbMATH Keywords: braid group
zbMATH Keywords: caterpillar graph
zbMATH Keywords: configuration space
zbMATH Keywords: linear tree
zbMATH Keywords: right-angled Artin group
MaRDI profile type: Publication
OpenAlex ID: W2094706661
arXiv ID: math/0411368
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DOI: 10.1007/S10711-013-9914-6
author: Francis Connolly
author: Margaret Doig
description: scientific article; zbMATH DE number 6358005