L2-Betti numbers of locally compact groups

Henrik Densing Petersen

L²-Betti numbers of locally compact groups

Henrik Densing Petersen

Abstract

We introduce a notion of L2-Betti numbers for locally compact, second countable, unimodular groups. We study the relation to the standard notion of L2-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 elds, and Kac-Moody lattices. We also extend the vanishing of reduced L2-cohomology for countable amenable groups, a well known theorem due to Cheeger and Gromov, to cover all amenable, second countable, unimodular locally compact groups.

Originalsprog	Engelsk

Forlag	Department of Mathematical Sciences, Faculty of Science, University of Copenhagen
Antal sider	139
ISBN (Trykt)	978-87-7078-993-6
Status	Udgivet - 2012

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Citationsformater

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