TY - JOUR
A2 - Rapinchuk, A.
A2 - Przybylska, M.
AU - Coskey, Samuel
PY - 2013
DA - 2013/12/30
TI - Ioana's Superrigidity Theorem and Orbit Equivalence Relations
SP - 387540
VL - 2013
AB - 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 this expository paper. In addition to a statement and proof of Ioana's theorem, this paper features the following: (i) an introduction to rigidity, including a crash course in Borel cocycles and a summaryof some of the best-known superrigidity theorems; (ii) some easy applications of superrigidity, both to ergodic theory (orbit equivalence)and set theory (Borel reducibility); and (iii) a streamlined proof of Simon Thomas's theorem that the classification of torsion-free abelian groups of finite rank is intractable.
SN - xxxx-xxxx
UR - https://doi.org/10.1155/2013/387540
DO - 10.1155/2013/387540
JF - ISRN Algebra
PB - Hindawi Publishing Corporation
KW -
ER -