Relative Property (T) for the Subequivalence Relations Induced by the Action of SL${}_2(\mathbb{Z})$ on ${\mathbb{T}}^2$

Adrian Ioana

Let $\Cal S$ be the equivalence relation induced by the action SL${}_2(\mathbb{Z})\curvearrowright ({\mathbb{T}}^2,{\lambda }^2)$, where ${\lambda }^2$ denotes the Haar measure on the 2-torus, ${\mathbb{T}}^2$. We pr…