Quasiflats in CAT(0) 2-complexes

Mladen Bestvina; Bruce Kleiner; Michah Sageev

doi:10.2140/agt.2016.16.2663

Quasiflats in CAT(0) 2-complexes

Mladen Bestvina, Bruce Kleiner, Michah Sageev

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	2663-2676
Number of pages	14
Journal	Algebraic and Geometric Topology
Volume	16
Issue number	5
DOIs	https://doi.org/10.2140/agt.2016.16.2663
State	Published - Nov 7 2016

Keywords

Piecewise Euclidean complex
Quasi-isometry
Quasiflat

ASJC Scopus subject areas

Geometry and Topology

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10.2140/agt.2016.16.2663

Cite this

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title = "Quasiflats in CAT(0) 2-complexes",

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 = "Piecewise Euclidean complex, Quasi-isometry, Quasiflat",

author = "Mladen Bestvina and Bruce Kleiner and Michah Sageev",

year = "2016",

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AU - Kleiner, Bruce

AU - Sageev, Michah

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N2 - 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.

AB - 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.

KW - Piecewise Euclidean complex

KW - Quasi-isometry

KW - Quasiflat

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Quasiflats in CAT(0) 2-complexes

Abstract

Keywords

ASJC Scopus subject areas

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