Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 4 (2016), 2229-2255.
$L^2$–invisibility of symmetric operad groups
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 . This can be applied, for example, to –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 .
Algebr. Geom. Topol., Volume 16, Number 4 (2016), 2229-2255.
Received: 21 July 2015
Accepted: 30 December 2015
First available in Project Euclid: 28 November 2017
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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