Ioana's superrigidity theorem and orbit equivalence relations
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 bestknown 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 torsionfree abelian groups of finite rank is intractable.
 Publication:

arXiv eprints
 Pub Date:
 October 2013
 arXiv:
 arXiv:1310.2359
 Bibcode:
 2013arXiv1310.2359C
 Keywords:

 Mathematics  Logic;
 Mathematics  Group Theory;
 37A20;
 20K15;
 03E15
 EPrint:
 This article is expository