Coarse equivalence and topological couplings of locally compact groups

Uri Bader; Christian Rosendal

doi:https://doi.org/10.1007/s10711-017-0300-7

Coarse equivalence and topological couplings of locally compact groups

Uri Bader, Christian Rosendal

Department of Mathematics

Weizmann Institute of Science

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

Abstract

M. Gromov has shown that any two finitely generated groups Γ and Λ are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions Γ ↷ X↶ Λ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second-countable groups.

Original language	English
Pages (from-to)	1-9
Number of pages	9
Journal	Geometriae Dedicata
Volume	196
Issue number	1
DOIs	https://doi.org/10.1007/s10711-017-0300-7
State	Published - 1 Oct 2018

Keywords

Coarse geometry
Locally compact groups
Topological couplings

All Science Journal Classification (ASJC) codes

Geometry and Topology

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https://doi.org/10.1007/s10711-017-0300-7

http://arxiv.org/pdf/1610.03004License: Unspecified

Cite this

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AB - M. Gromov has shown that any two finitely generated groups Γ and Λ are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions Γ ↷ X↶ Λ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second-countable groups.

KW - Coarse geometry

KW - Locally compact groups

KW - Topological couplings

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Coarse equivalence and topological couplings of locally compact groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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