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

Volume 243 / 2018

Roman Sauer, Michael Schrödl 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.

Authors

  • Roman SauerInstitute for Algebra and Geometry
    Karlsruhe Institute of Technology
    Englerstr. 2
    76128 Karlsruhe, Germany
    e-mail
  • Michael SchrödlInstitute for Algebra and Geometry
    Karlsruhe Institute of Technology
    Englerstr. 2
    76128 Karlsruhe, Germany
    e-mail

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