L2-Betti numbers of locally compact groups
Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
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L2-Betti numbers of locally compact groups. / Petersen, Henrik Densing.
Department of Mathematical Sciences, Faculty of Science, University of Copenhagen, 2012. 139 s.Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
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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://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122937157505763
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 -
ID: 92325784