Vanishing of $\ell ^2$-Betti numbers of locally compact groups as an invariant of coarse equivalence
Volume 243 / 2018
Fundamenta Mathematicae 243 (2018), 301-311
MSC: Primary 20F65; Secondary 22D99.
DOI: 10.4064/fm512-1-2018
Published online: 29 June 2018
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. To this end, we define coarse $\ell ^2$-cohomology for locally compact groups and show that it is isomorphic to continuous cohomology for unimodular groups and invariant under coarse equivalence.
