Quasi-isometric classification of right-angled Artin groups, I: The finite out case

Huang, Jingyin

doi:10.2140/gt.2017.21.3467

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Quasi-isometric classification of right-angled Artin groups, I: The finite out case

Jingyin Huang

Geometry & Topology 21 (2017) 3467–3537

DOI: 10.2140/gt.2017.21.3467

Abstract

Let $G$ and $G^{'}$ be two right-angled Artin groups. We show they are quasi-isometric if and only if they are isomorphic, under the assumption that the outer automorphism groups $Out (G)$ and $Out (G^{'})$ are finite. If we only assume $Out (G)$ is finite, then $G^{'}$ is quasi-isometric to $G$ if and only if $G^{'}$ is isomorphic to a subgroup of finite index in $G$ . In this case, we give an algorithm to determine whether $G$ and $G^{'}$ are quasi-isometric by looking at their defining graphs.

Keywords

quasi-isometric classification, right-angled Artin groups, extension complexes, generalized star extension

Mathematical Subject Classification 2010

Primary: 20F65, 20F67, 20F69

References

Publication

Received: 4 November 2015

Revised: 16 September 2016

Accepted: 25 November 2016

Published: 31 August 2017

Proposed: Walter Neumann

Seconded: Dmitri Burago, Bruce Kleiner

Authors

Jingyin Huang
The Department of Mathematics and Statistics McGill University Montreal, QC Canada

Volume 21, issue 6 (2017)