W$^*$-superrigidity for wreath products with groups having positive first $\ell^2$-Betti number
In [BV12] we have proven that, for all hyperbolic groups and for all non-trivial free products $Γ$, the left-right wreath product group $G:=(Z/2Z)^{(Γ)} \rtimes (Γ\times Γ)$ is W$^*$-superrigid. In this paper, we extend this result to other classes of countable groups. More precisely, we prove that for weakly amenable groups $Γ$ having positive first $\ell^2$-Betti number, the same wreath product $G$ is W$^*$-superrigid.
math.OA↗