Proceedings of the International Congress of Mathematicians
Madrid, August 22–30, 2006

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pp: 445–477

DOI: 10.4171/022-1/18

Deformation and rigidity for group actions and von Neumann algebras

Sorin Popa[1]

(1) Department of Mathematics, University of California Los Angeles, Box 951555, CA 90095-1555, LOS ANGELES, UNITED STATES

We present some recent rigidity results for von Neumann algebras (II1 factors) and equivalence relations arising from measure preserving actions of groups on probability spaces which satisfy a combination of deformation and rigidity properties. This includes strong rigidity results for factors with calculation of their fundamental group and cocycle superrigidity for actions with applications to orbit equivalence ergodic theory.

Keywords: von Neumann algebras, II1 factors, amenability and property T for groups, measure preserving actions, Bernoulli actions, orbit equivalence, cocycles