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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The asymptotic geometry of right-angled Artin groups, I

Mladen Bestvina, Bruce Kleiner and Michah Sageev

Geometry & Topology 12 (2008) 1653–1699
Abstract

We study atomic right-angled Artin groups – those whose defining graph has no cycles of length 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