Non-Orbit Equivalent Actions of $\Bbb F_n$

Abstract

For any $2\leq n\leq \infty$, we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group $\Bbb F_n$. These actions arise as diagonal products between a generalized Bernoulli action and the action $\Bbb F_n\curvearrowright (\Bbb T^2,\lambda^2)$, where $\Bbb F_n$ is seen as a subgroup of SL$_2(\Bbb Z)$.