Cocycle superrigidity for coinduced actions

Abstract

We prove a cocycle superrigidity theorem for a large class of coinduced actions. In particular, if $\Lambda$ is a subgroup of a countable group $\Gamma$, we consider a probability measure preserving action $\Lambda \curvearrowright X_0$ and let $\Gamma \curvearrowright X$ be the coinduced action. Assume either that $\Gamma$ has property (T) or that $\Lambda$ is amenable and $\Gamma$ is a product of non-amenable groups. Using Popa's deformation/rigidity theory we prove $\Gamma \curvearrowright X$ is ${\mathcal{U}}_{fin}$-cocycle superrigid, that is any cocycle for this action to a ${\mathcal{U}}_{fin}$ (e.g. countable) group $\mathcal{V}$ is cohomologous to a homomorphism from $\Gamma$ to $\mathcal{V}.$

References in corpus (2)

• Examples of group actions which are virtually W*-superrigid
• OE and W* superrigidity results for actions by surface braid groups