On the Superrigidity of Malleable Actions with Spectral Gap
نویسنده
چکیده
We prove that if a countable group Γ contains a non-amenable subgroup with centralizer infinite and “weakly normal” in Γ (e.g. if Γ is non-amenable and has infinite center or is a product of infinite groups) then any measure preserving Γ-action on a probability space which satisfies certain malleability, spectral gap and weak mixing conditions is cocycle superrigid. We also show that if Γ y X is an arbitrary free ergodic action of such a group Γ and Λ y Y = [0, 1] is a Bernoulli action of an arbitrary infinite conjugacy class group, then any isomorphism of the associated II1 factors L ∞X ⋊Γ ≃ L∞Y ⋊Λ comes from a conjugacy of the actions.
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COCYCLE SUPERRIGIDITY FOR MALLEABLE ACTIONS WITH SPECTRAL GAP Preliminary version
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