Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups

Abstract

We study equivalence relations and II 1 factors associated with (quotients of) generalized Bernoulli actions of Kazhdan groups. Specific families of these actions are entirely classified up to isomorphism of II 1 factors. This yields explicit computations of outer automorphism and fundamental groups. In particular, every finitely presented group is concretely realized as the outer automorphism group of a continuous family of non stably isomorphic II 1 factors.