Coarse equivalence and topological couplings of locally compact groups

2016/10/10 by Bader, Uri, Rosendal, Christian
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1610.03004

Abstract

A result due to M. Gromov states 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\curvearrowright X\curvearrowleft Λ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second countable groups.

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