Algebraic & Geometric Topology

$L^2$–invisibility of symmetric operad groups

Werner Thumann

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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 .

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 4 (2016), 2229-2255.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1511895913

Digital Object Identifier
doi:10.2140/agt.2016.16.2229

Mathematical Reviews number (MathSciNet)
MR3546464

Zentralblatt MATH identifier
06627574

Subjects
Primary: 20J05: Homological methods in group theory
Secondary: 22D10: Unitary representations of locally compact groups 18D50: Operads [See also 55P48]

Keywords
operad groups Thompson groups group homology L2-homology

Citation

Thumann, Werner. $L^2$–invisibility of symmetric operad groups. Algebr. Geom. Topol. 16 (2016), no. 4, 2229--2255. doi:10.2140/agt.2016.16.2229. https://projecteuclid.org/euclid.agt/1511895913


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