Non-Orbit Equivalent Actions of ${\mathbb{F}}_n$

Abstract

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

final version

References in corpus (1)

• Orbit inequivalent actions of non-amenable groups

Cited by in corpus (1)

• On a class of ${\mathrm{II}}_1$ factors with at most one Cartan subalgebra