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Weak notions of normality and vanishing up to rank in L2-cohomology

By Uri Bader, Alex Furman and Roman Sauer

Abstract

We study vanishing results for L2-cohomology of countable groups under the presence of subgroups that satisfy some weak normality condition. As a consequence we show that the L2-Betti numbers of SL(n,R) for any infinite integral domain R vanish below degree n-1. We also give a uniform proof for the vanishing of L2-Betti numbers of Thompson's groups F and T.Comment: Final versio

Topics: Mathematics - Group Theory, Mathematics - Algebraic Topology, 20J05, 37A20
Year: 2013
DOI identifier: 10.1093/imrn/rnt029
OAI identifier: oai:arXiv.org:1206.4793

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