Algebraic & Geometric Topology

$L^2$–invisibility of symmetric operad groups

Werner Thumann

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
Accepted: 30 December 2015
First available in Project Euclid: 28 November 2017

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

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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