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Summary: Countable Borel Equivalence Relations:
The Appendix
Simon Thomas
Rutgers University
17th November 2007
Simon Thomas (Rutgers University) Appalachian Set Theory Workshop 17th November 2007
Popa's Cocycle Superrigidity Theorem
In this lecture, we shall sketch the proof of:
Theorem (Popa)
Let be a countably infinite Kazhdan group and let G be a countable
group such that G. If H is any countable group, then every Borel
cocycle
: G × 2G
H
is equivalent to a group homomorphism of G into H.
Remark
Popa's original proof was written in the framework of Operator
Algebras.
This presentation is based upon Furman's Ergodic-theoretic
account.
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