On the Superrigidity of Malleable Actions with Spectral Gap
| dc.creator | Popa, Sorin | |
| dc.date | 2006-08-16 | |
| dc.date | 2007-12-25 | |
| dc.date.accessioned | 2026-07-07T08:50:58Z | |
| dc.date.available | 2026-07-07T08:50:58Z | |
| dc.description | We prove that if a countable group $Γ$ contains infinite commuting subgroups $H, H'\subset Γ$ with $H$ non-amenable and $H'$ ``weakly normal'' in $Γ$, then any measure preserving $Γ$-action on a probability space which satisfies certain malleability, spectral gap and weak mixing conditions (e.g. a Bernoulli $Γ$-action) is cocycle superrigid. If in addition $H'$ can be taken non-virtually abelian and $Γ\curvearrowright X$ is an arbitrary free ergodic action while $Λ\curvearrowright Y=\Bbb T^Λ$ is a Bernoulli action of an arbitrary infinite conjugacy class group, then any isomorphism of the associated II$_1$ factors $L^\infty X \rtimes Γ\simeq L^\infty Y \rtimes Λ$ comes from a conjugacy of the actions. | |
| dc.description | Final version; paper appeared in Journal of the Amer. Math. Soc., 2007 | |
| dc.identifier | https://arxiv.org/abs/math/0608429 | |
| dc.identifier | http://arxiv.org/abs/math/0608429 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144783 | |
| dc.subject | Group Theory | |
| dc.subject | Operator Algebras | |
| dc.subject | 28D15, 46L10, 46L35, 20E05 | |
| dc.title | On the Superrigidity of Malleable Actions with Spectral Gap | |
| dc.type | text |