Continuous cocycle superrigidity for coinduced actions and relative ends
نویسندگان
چکیده
منابع مشابه
On cocycle superrigidity for Gaussian actions
We present a general setting to investigate Ufin-cocycle superrigidity for Gaussian actions in terms of closable derivations on von Neumann algebras. In this setting we give new proofs to some Ufin-cocycle superrigidity results of S. Popa and we produce new examples of this phenomenon. We also use a result of K. R. Parthasarathy and K. Schmidt to give a necessary cohomological condition on a gr...
متن کاملCocycle Superrigidity for Ergodic Actions of Non-semisimple Lie Groups
Suppose L is a semisimple Levi subgroup of a connected Lie group G, X is a Borel G-space with finite invariant measure, and α : X × G → GLn(R) is a Borel cocycle. Assume L has finite center, and that the real rank of every simple factor of L is at least two. We show that if L is ergodic on X, and the restriction of α to X × L is cohomologous to a homomorphism (modulo a compact group), then, aft...
متن کاملCOCYCLE SUPERRIGIDITY FOR MALLEABLE ACTIONS WITH SPECTRAL GAP Preliminary version
Let Γ y X be a measure preserving (m.p.) action of a discrete group Γ on a probability measure space (X,μ) and H ⊂ Γ a non-amenable subgroup with commutant H = {g ∈ Γ | gh = hg, ∀h ∈ H} infinite. We prove that if the action satisfies a malleability condition on HH, is weak mixing on H and has stable spectral gap on H (e.g. if the action is Bernoulli on HH), then any cocycle with values in a Pol...
متن کاملOn Popa’s Cocycle Superrigidity Theorem
Theorem 1.1 (Popa’s Cocycle Superrigity, Special Case). Let Γ be a discrete group with Kazhdan’s property (T), let Γ0 < Γ be an infinite index subgroup, (X0,μ0) an arbitrary probability space, and let Γ (X,μ) = (X0,μ0)0 be the corresponding generalized Bernoulli action. Then for any discrete countable group Λ and any measurable cocycle α : Γ × X → Λ there exist a homomorphism : Γ → Λ and a meas...
متن کاملCOCYCLE AND ORBIT EQUIVALENCE SUPERRIGIDITY FOR MALLEABLE ACTIONS OF w-RIGID GROUPS
We prove that if a countable discrete group Γ is w-rigid, i.e. it contains an infinite normal subgroup H with the relative property (T) (e.g. Γ = SL(2,Z) ⋉Z, or Γ = H × H with H an infinite Kazhdan group and H arbitrary), and V is a closed subgroup of the group of unitaries of a finite separable von Neumann algebra (e.g. V countable discrete, or separable compact), then any V-valued measurable ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2018
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14260