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L^2-Betti Numbers of Locally Compact Groups

By Henrik Densing Petersen

Abstract

We introduce a notion of $L^2$-Betti numbers for locally compact, second countable, unimodular groups. We study the relation to the standard notion of $L^2$-Betti numbers of countable discrete groups for lattices. In this way, several new computations are obtained for countable groups, including lattices in algebraic groups over local fields, and Kac-Moody lattices. We also extend the vanishing of reduced $L^2$-cohomology for countable amenable groups, a well known theorem due to Cheeger and Gromov, to cover all amenable, second countable, unimodular locally compact groups.Comment: The latest update replaces the old preprint with the authors thesis. This is the final versio

Topics: Mathematics - Group Theory, 20J06, 22F30, 22E40, 22E41, 57T10
Year: 2013
OAI identifier: oai:arXiv.org:1104.3294
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