Coarse equivalence and topological couplings of locally compact groups

Uri Bader; Christian Rosendal

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arXiv · 1610.03004

Coarse equivalence and topological couplings of locally compact groups

Uri Bader·Christian Rosendal

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Abstract

A result due to M. Gromov states that any two finitely generated groups {\Gamma} and {\Lambda} are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions $\Gamma\curvearrowright X\curvearrowleft \Lambda$ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second countable groups.

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Uri Bader, Christian Rosendal. 2016-10-10. Coarse equivalence and topological couplings of locally compact groups. https://arxiv.org/abs/1610.03004

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