On Popa's Cocycle Superrigidity Theorem

Abstract

These notes contain an Ergodic-theoretic account of the Cocycle Superrigidity Theorem recently discovered by Sorin Popa. We state and prove a relative version of the result, discuss some applications to measurable equivalence relations, and point out that Gaussian actions (of ``rigid'' groups) satisfy the assumptions of Popa's theorem.

v.2: slight changes in the presentation, (some) typos corrected, wq-normal subgroups added. 35 pages

References in corpus (5)

• Outer automorphism groups of some ergodic equivalence relations
• Amalgamated Free Products of $w$-Rigid Factors and Calculation of their Symmetry Groups
• Rigidity results for Bernoulli actions and their von Neumann algebras (after Sorin Popa)
• On the Cohomology of Actions of Groups by Bernoulli Shifts
• Cocycle and Orbit Equivalence Superrigidity for Malleable Actions of w-Rigid Groups

Cited by in corpus (3)

• OE and W* superrigidity results for actions by surface braid groups
• Cocycle and Orbit Equivalence Superrigidity for Malleable Actions of w-Rigid Groups
• On the Superrigidity of Malleable Actions with Spectral Gap