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Cocycle superrigidity for coinduced actions
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Cocycle superrigidity for coinduced actions

Daniel Drimbe
ArXiv.org
Cornell University
11/30/2015
DOI: 10.48550/arxiv.1512.00093
url
https://doi.org/10.1017/etds.2016.134View
Published (Version of record)This article has now been published in a journal and has been peer-reviewed by subject experts. This version may differ significantly from the preprint version. Access restricted to faculty, staff and students
url
https://doi.org/10.48550/arxiv.1512.00093View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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Abstract

We prove a cocycle superrigidity theorem for a large class of coinduced actions. In particular, if Λ is a subgroup of a countable group Γ, we consider a probability measure preserving action Λ↷X0 and let Γ↷X be the coinduced action. Assume either that Γ has property (T) or that Λ is amenable and Γ is a product of non-amenable groups. Using Popa's deformation/rigidity theory we prove Γ↷X is Ufin-cocycle superrigid, that is any cocycle for this action to a Ufin (e.g. countable) group V is cohomologous to a homomorphism from Γ to V.
 Mathematics - Dynamical Systems Mathematics - Operator Algebras

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