Duke Mathematical Journal

Cocycle superrigidity for profinite actions of property (T) Groups

Adrian Ioana

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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.

Article information

Source
Duke Math. J., Volume 157, Number 2 (2011), 337-367.

Dates
First available in Project Euclid: 25 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1301059111

Digital Object Identifier
doi:10.1215/00127094-2011-008

Mathematical Reviews number (MathSciNet)
MR2783933

Zentralblatt MATH identifier
1235.37005

Subjects
Primary: 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
Secondary: 28D15: General groups of measure-preserving transformations 46L36: Classification of factors

Citation

Ioana, Adrian. Cocycle superrigidity for profinite actions of property (T) Groups. Duke Math. J. 157 (2011), no. 2, 337--367. doi:10.1215/00127094-2011-008. https://projecteuclid.org/euclid.dmj/1301059111


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