On the superrigidity of malleable actions with spectral gap
نویسندگان
چکیده
منابع مشابه
On the Superrigidity of Malleable Actions with Spectral Gap
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 i...
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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...
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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 ...
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This paper proves various results concerning nonergodic actions of locally compact groups and particularly Borel cocycles defined over such actions. The general philosophy is to reduce the study of the cocycle to the study of its restriction to each ergodic component of the action, while being careful to show that all objects arising in the analysis depend measurably on the ergodic component. T...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2007
ISSN: 0894-0347
DOI: 10.1090/s0894-0347-07-00578-4