  We show a homological result for the class of planar or symmetric operad
groups: We show that 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 $l^2$-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 $nV$.

Algebraic Topology;Group Theory