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1 April 2011 Cocycle superrigidity for profinite actions of property (T) Groups
Adrian Ioana
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Duke Math. J. 157(2): 337-367 (1 April 2011). DOI: 10.1215/00127094-2011-008

Abstract

Consider a free ergodic measure-preserving profinite action ΓX (i.e., an inverse limit of actions ΓXn, with Xn finite) of a countable property (T) group Γ (more generally, of a group Γ which admits an infinite normal subgroup Γ0 such that the inclusion Γ0Γ has relative property (T) and Γ/Γ0 is finitely generated) on a standard probability space X. We prove that if w:Γ×XΛ is a measurable cocycle with values in a countable group Λ, then w is cohomologous to a cocycle w which factors through the map Γ×XΓ×Xn, for some n. As a corollary, we show that any orbit equivalence of ΓX with any free ergodic measure-preserving action ΛY comes from a (virtual) conjugacy of actions.

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Adrian Ioana. "Cocycle superrigidity for profinite actions of property (T) Groups." Duke Math. J. 157 (2) 337 - 367, 1 April 2011. https://doi.org/10.1215/00127094-2011-008

Information

Published: 1 April 2011
First available in Project Euclid: 25 March 2011

zbMATH: 1235.37005
MathSciNet: MR2783933
Digital Object Identifier: 10.1215/00127094-2011-008

Subjects:
Primary: 37A20
Secondary: 28D15, 46L36

Rights: Copyright © 2011 Duke University Press

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Vol.157 • No. 2 • 1 April 2011
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