Quasiflats in CAT(0) 2–complexes

Bestvina, Mladen; Kleiner, Bruce; Sageev, Michah

doi:10.2140/agt.2016.16.2663

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Quasiflats in $\mathrm{CAT}(0)$ $2$–complexes

Mladen Bestvina, Bruce Kleiner and Michah Sageev

Algebraic & Geometric Topology 16 (2016) 2663–2676

DOI: 10.2140/agt.2016.16.2663

Abstract

We show that if $X$ is a piecewise Euclidean $2$ –complex with a cocompact isometry group, then every $2$ –quasiflat in $X$ is at finite Hausdorff distance from a subset $Q$ which is locally flat outside a compact set, and asymptotically conical.

Keywords

quasi-isometry, quasiflat, piecewise Euclidean complex

Mathematical Subject Classification 2010

Primary: 20F65

References

Publication

Received: 22 October 2014

Revised: 26 May 2015

Accepted: 21 June 2015

Published: 7 November 2016

Authors

Mladen Bestvina
Department of Mathematics University of Utah Salt Lake City, UT 84112-0090 United States

Bruce Kleiner
Courant Institute of Mathematical Sciences 251 Mercer St New York, NY 10012 United States

Michah Sageev
Department of Mathematics Israel Institute of Technology 32000 Haifa Israel

Volume 16, issue 5 (2016)