Geodesic
L2–invisibility of symmetric operad groups
Thumann, Werner1
1Department of Mathematics, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany
Algebraic and Geometric Topology, Tome 16 (2016) no. 4, pp. 2229-2255
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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 .

DOI : 10.2140/agt.2016.16.2229
Classification : 20J05, 22D10, 18D50
Keywords: operad groups, Thompson groups, group homology, L2-homology

Thumann, Werner  1

1 Department of Mathematics, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany 
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Thumann, Werner. L2–invisibility of symmetric operad groups. Algebraic and Geometric Topology, Tome 16 (2016) no. 4, pp. 2229-2255. doi: 10.2140/agt.2016.16.2229

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