Relative Property (T) for the Subequivalence Relations Induced by the Action of SL$_2(\Bbb Z)$ on $\Bbb T^2$
| dc.creator | Ioana, Adrian | |
| dc.date | 2009-01-13 | |
| dc.date.accessioned | 2026-07-07T12:29:04Z | |
| dc.date.available | 2026-07-07T12:29:04Z | |
| dc.description | Let $\Cal S$ be the equivalence relation induced by the action SL$_2(\Bbb Z)\curvearrowright (\Bbb T^2,λ^2)$, where $λ^2$ denotes the Haar measure on the 2-torus, $\Bbb T^2$. We prove that any ergodic subequivalence relation $\Cal R$ of $\Cal S$ is either hyperfinite or rigid in the sense of S. Popa ([Po06]). The proof uses an ergodic-theoretic criterion for rigidity of countable, ergodic, probability measure preserving equivalence relations. Moreover, we give a purely ergodic-theoretic formulation of rigidity for free, ergodic, probability measure preserving actions of countable groups. | |
| dc.identifier | https://arxiv.org/abs/0901.1874 | |
| dc.identifier | http://arxiv.org/abs/0901.1874 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215750 | |
| dc.subject | Operator Algebras | |
| dc.subject | Dynamical Systems | |
| dc.subject | Group Theory | |
| dc.title | Relative Property (T) for the Subequivalence Relations Induced by the Action of SL$_2(\Bbb Z)$ on $\Bbb T^2$ | |
| dc.type | text |