Non-orbit equivalent actions of ${𝔽}_n$

Ioana, Adrian

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 4, pp. 675-696.

Pour tout $2\le n\le \infty$, nous construisons une famille concrète à un paramètre, des actions non orbitalement équivalentes du groupe libre ${𝔽}_n$. Ces actions apparaissent comme produits diagonaux entre une action généralisée de Bernoulli et l’action ${𝔽}_n\curvearrowright ({𝕋}^2,{\lambda }^2)$, où ${𝔽}_n$ est vu comme un sous-groupe de ${\mathrm{SL}}_2\left(\mathbb{Z}\right)$.

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

Classification : 37A20, 46L10
Keywords: free groups, orbit equivalence
Mot clés : groupes libres, équivalence orbitale

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