L²-Betti numbers of locally compact groups

TY - BOOK

T1 - L2-Betti numbers of locally compact groups

AU - Petersen, Henrik Densing

PY - 2012

Y1 - 2012

N2 - 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 latticesin 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.

AB - 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 latticesin 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.

UR - https://rex.kb.dk/primo-explore/fulldisplay?docid=KGL01009117531&context=L&vid=NUI&search_scope=KGL&tab=default_tab&lang=da_DK

M3 - Ph.D. thesis

SN - 978-87-7078-993-6

BT - L2-Betti numbers of locally compact groups

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -