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

[Actions non orbitalement équivalentes de $\mathbb {F}_n$]

Ioana, Adrian

Annales scientifiques de l'École Normale Supérieure, Tome 42 (2009), p. 675-696 / Harvested from Numdam

Résumé

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

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 $\mathrm {SL}_2(\mathbb {Z})$.

Détail

Publié le : 2009-01-01

MR 2568879 | Zbl 1185.37009

DOI : https://doi.org/10.24033/asens.2106
Classification:  37A20,  46L10
Mots clés: groupes libres, équivalence orbitale

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