#### Volume 12, issue 3 (2008)

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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
##### Abstract

We study atomic right-angled Artin groups – those whose defining graph has no cycles of length $\le 4$, 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
##### 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