On the Superrigidity of Malleable Actions with Spectral Gap

Details On the Superrigidity of Malleable Actions with Spectral Gap On the Superrigidity of Malleable Actions with Spectral Gap

2006-08-16

arxiv.org/abs/math/0608429v6

Mathematics

Group Theory

Final version; paper appeared in Journal of the Amer. Math. Soc., 2007

Scientific paper

We prove that if a countable group $\Gamma$ contains infinite commuting subgroups $H, H'\subset \Gamma$ with $H$ non-amenable and $H'$ ``weakly normal'' in $\Gamma$, then any measure preserving $\Gamma$-action on a probability space which satisfies certain malleability, spectral gap and weak mixing conditions (e.g. a Bernoulli $\Gamma$-action) is cocycle superrigid. If in addition $H'$ can be taken non-virtually abelian and $\Gamma \curvearrowright X$ is an arbitrary free ergodic action while $\Lambda \curvearrowright Y=\Bbb T^\Lambda$ is a Bernoulli action of an arbitrary infinite conjugacy class group, then any isomorphism of the associated II$_1$ factors $L^\infty X \rtimes \Gamma \simeq L^\infty Y \rtimes \Lambda$ comes from a conjugacy of the actions.

Affiliated with

Also associated with

No associations

Rating

On the Superrigidity of Malleable Actions with Spectral Gap does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Superrigidity of Malleable Actions with Spectral Gap, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Superrigidity of Malleable Actions with Spectral Gap will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-388953