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 .
"$L^2$–invisibility of symmetric operad groups." Algebr. Geom. Topol. 16 (4) 2229 - 2255, 2016. https://doi.org/10.2140/agt.2016.16.2229