A RIGIDITY RESULT FOR ACTIONS OF PROPERTY T GROUPS BY BERNOULLI SHIFTS

SORIN POPA

Abstract. Let σ be the action of an infinite property T group G on the hyperfinite type II_{1} factor R = \overline{∈_{g} G → ⊗}(M_{2×2}(ℂ), tr)_{g}, by Bernoulli shifts. We prove that

the cocycle actions obtained by reducing σ to the algebras pRp, for p non-trivial projections in R, cannot be perturbed to actions. We also prove that any 1-cocycle for σ vanishes. More generally, we calculate all 1-cocycles for actions of property T groups G by Bernoulli shifts of Connes-Størmer type and use this to provide an invariant that distinguishes these actions up to cocycle conjugacy.