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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2013
- arXiv:
- arXiv:1310.2359
- Bibcode:
- 2013arXiv1310.2359C
- Keywords:
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- Mathematics - Logic;
- Mathematics - Group Theory;
- 37A20;
- 20K15;
- 03E15
- E-Print:
- This article is expository