Duke Mathematical Journal
- Duke Math. J.
- Volume 157, Number 2 (2011), 337-367.
Cocycle superrigidity for profinite actions of property (T) Groups
Consider a free ergodic measure-preserving profinite action (i.e., an inverse limit of actions , with finite) of a countable property (T) group (more generally, of a group which admits an infinite normal subgroup such that the inclusion has relative property (T) and is finitely generated) on a standard probability space . We prove that if is a measurable cocycle with values in a countable group , then is cohomologous to a cocycle which factors through the map , for some . As a corollary, we show that any orbit equivalence of with any free ergodic measure-preserving action comes from a (virtual) conjugacy of actions.
Duke Math. J., Volume 157, Number 2 (2011), 337-367.
First available in Project Euclid: 25 March 2011
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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