The asymptotic geometry of right-angled Artin groups, I

Bestvina, Mladen; Kleiner, Bruce; Sageev, Michah

doi:10.2140/gt.2008.12.1653

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The asymptotic geometry of right-angled Artin groups, I

Mladen Bestvina, Bruce Kleiner and Michah Sageev

Geometry & Topology 12 (2008) 1653–1699

DOI: 10.2140/gt.2008.12.1653

Abstract

We study atomic right-angled Artin groups – those whose defining graph has no cycles of length $\leq 4$ , and no separating vertices, separating edges, or separating vertex stars. We show that these groups are not quasi-isometrically rigid, but that an intermediate form of rigidity does hold. We deduce from this that two atomic groups are quasi-isometric iff they are isomorphic.

Keywords

CAT(0), quasi-isometry, rigidity

Mathematical Subject Classification 2000

Primary: 20F65, 20F69

Secondary: 20F67, 05C25

References

Publication

Received: 15 September 2007

Accepted: 1 April 2008

Published: 19 June 2008

Proposed: Benson Farb

Seconded: Walter Neumann, Martin Bridson

Authors

Mladen Bestvina
Department of Mathematics University of Utah 155 South 1400 East, Room 233 Salt Lake City, UT 84112-0090

Bruce Kleiner
Yale University Mathematics Department PO Box 208283 New Haven, CT 06520-8283

Michah Sageev
Department of Mathematics Technion – Israel Institute of Technology Haifa 32000, Israel

Volume 12, issue 3 (2008)