$L^2$-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices

Abstract

The main result is a general approximation theorem for normalised Betti numbers for Farber sequences of lattices in totally disconnected groups. Further, we contribute some computations and complements to the general theory of $L^2$-Betti numbers of totally disconnected groups.

final version; accepted for publication by the Journal of Topology

References in corpus (3)

• Vanishing of ${\ell }^2$-Betti numbers of locally compact groups as an invariant of coarse equivalence
• L^2-Betti Numbers of Discrete Measured Groupoids
• l2-Betti numbers of discrete and non-discrete groups

Cited by in corpus (7)

• Vanishing of ${\ell }^2$-Betti numbers of locally compact groups as an invariant of coarse equivalence
• Graphs and complexes of lattices
• Rational discrete first degree cohomology for totally disconnected locally compact groups
• ${\ell }^2$-Betti numbers of random rooted simplicial complexes
• A note on the rational homological dimension of lattices in positive characteristic
• Double-coset zeta functions for groups acting on trees
• On homological properties of the Schlichting completion