Ioana's superrigidity theorem and orbit equivalence relations

Samuel Coskey

doi:10.1155/2013/387540

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arXiv · 1310.2359

Ioana's superrigidity theorem and orbit equivalence relations

Samuel Coskey

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Abstract

In this expository article, we give a survey of Adrian Ioana's cocycle superrigidity theorem for profinite actions of Property (T) groups, and its applications to ergodic theory and set theory. In addition to a statement and proof of Ioana's theorem, this article features: * An introduction to rigidity, including a crash course in Borel cocycles and a summary of some of the best-known superrigidity theorems; * Some easy applications of superrigidity, both to ergodic theory (orbit equivalence) and set theory (Borel reducibility); and * A streamlined proof of Simon Thomas's theorem that the classification of torsion-free abelian groups of finite rank is intractable.

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Samuel Coskey. 2013-10-09. Ioana's superrigidity theorem and orbit equivalence relations. https://doi.org/10.1155/2013/387540

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