Volume 16, issue 5 (2016)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Quasiflats in $\mathrm{CAT}(0)$ $2$–complexes

Mladen Bestvina, Bruce Kleiner and Michah Sageev

Algebraic & Geometric Topology 16 (2016) 2663–2676
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