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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
$L^2$–invisibility of symmetric operad groups

Werner Thumann

Algebraic & Geometric Topology 16 (2016) 2229–2255
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 l2–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 nV .

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