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

Jingyin Huang

Geometry & Topology 21 (2017) 3467–3537

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.

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quasi-isometric classification, right-angled Artin groups, extension complexes, generalized star extension
Mathematical Subject Classification 2010
Primary: 20F65, 20F67, 20F69
Received: 4 November 2015
Revised: 16 September 2016
Accepted: 25 November 2016
Published: 31 August 2017
Proposed: Walter Neumann
Seconded: Dmitri Burago, Bruce Kleiner
Jingyin Huang
The Department of Mathematics and Statistics
McGill University
Montreal, QC