Bi-exact Wreath-like Product Groups

Abstract

In this short paper, we prove the bi-exactness of all wreath-like product groups $G\in \mathcal{WR}(A,B\curvearrowright I)$, whenever $A$ is amenable, $B$ is bi-exact, and the action $B\curvearrowright I$ has amenable stabilizers. As applications, we obtain solidity for the associated group von Neumann algebras and, by combining our result with existing rigidity theorems, new examples exhibiting the McDuff superrigidity.

11 pages