Volume 16, issue 5 (2016)

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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
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
Primary: 20F65