On the Superrigidity of Malleable Actions with Spectral Gap

dc.creatorPopa, Sorin
dc.date2006-08-16
dc.date2007-12-25
dc.date.accessioned2026-07-07T08:50:58Z
dc.date.available2026-07-07T08:50:58Z
dc.descriptionWe 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.descriptionFinal version; paper appeared in Journal of the Amer. Math. Soc., 2007
dc.identifierhttps://arxiv.org/abs/math/0608429
dc.identifierhttp://arxiv.org/abs/math/0608429
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144783
dc.subjectGroup Theory
dc.subjectOperator Algebras
dc.subject28D15, 46L10, 46L35, 20E05
dc.titleOn the Superrigidity of Malleable Actions with Spectral Gap
dc.typetext

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