L2–invisibility of symmetric operad groups

Thumann, Werner

doi:10.2140/agt.2016.16.2229

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$L^2$–invisibility of symmetric operad groups

Werner Thumann

Algebraic & Geometric Topology 16 (2016) 2229–2255

DOI: 10.2140/agt.2016.16.2229

Abstract

We show a homological result for the class of planar or symmetric operad groups: under certain conditions, group (co)homology of such groups with certain coefficients vanishes in all dimensions, provided it vanishes in dimension $0$ . This can be applied, for example, to $l^{2}$ –homology or cohomology with coefficients in the group ring. As a corollary, we obtain explicit vanishing results for Thompson-like groups such as the Brin–Thompson groups $n V$ .

Keywords

operad groups, Thompson groups, group homology, L2-homology

Mathematical Subject Classification 2010

Primary: 20J05

Secondary: 22D10, 18D50

References

Publication

Received: 21 July 2015

Accepted: 30 December 2015

Published: 12 September 2016

Authors

Werner Thumann
Department of Mathematics Karlsruhe Institute of Technology D-76128 Karlsruhe Germany

Volume 16, issue 4 (2016)