Vanishing of ${\ell }^2$-Betti numbers of locally compact groups as an invariant of coarse equivalence

Abstract

We provide a proof that the vanishing of ${\ell }^2$-Betti numbers of unimodular locally compact second countable groups is an invariant of coarse equivalence.

Added Remark 13, to appear in Fundamenta Mathematicae

References in corpus (3)

• $L^2$-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices
• L^2-Betti Numbers of Discrete Measured Groupoids
• Group approximation in Cayley topology and coarse geometry, Part III: Geometric property (T)

Cited by in corpus (4)

• Cantor systems and quasi-isometry of groups
• $L^2$-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices
• Quasi-isometric invariance of continuous group $L^p$-cohomology, and first applications to vanishings
• Dynamic characterizations of quasi-isometry, and applications to cohomology