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2016 $L^2$–invisibility of symmetric operad groups
Werner Thumann
Algebr. Geom. Topol. 16(4): 2229-2255 (2016). 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 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 .

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Werner Thumann. "$L^2$–invisibility of symmetric operad groups." Algebr. Geom. Topol. 16 (4) 2229 - 2255, 2016. https://doi.org/10.2140/agt.2016.16.2229

Information

Received: 21 July 2015; Accepted: 30 December 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 06627574
MathSciNet: MR3546464
Digital Object Identifier: 10.2140/agt.2016.16.2229

Subjects:
Primary: 20J05
Secondary: 18D50, 22D10

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.16 • No. 4 • 2016
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