Coarse equivalence and topological couplings of locally compact groups
Group Theory
2016-10-11 v1
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 on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second countable groups.
Cite
@article{arxiv.1610.03004,
title = {Coarse equivalence and topological couplings of locally compact groups},
author = {Uri Bader and Christian Rosendal},
journal= {arXiv preprint arXiv:1610.03004},
year = {2016}
}