Non-orbit equivalent actions of 𝔽 n
[Actions non orbitalement équivalentes de 𝔽 n ]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 4, pp. 675-696.

Pour tout 2n, 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 (𝕋 2 ,λ 2 ), où 𝔽 n est vu comme un sous-groupe de SL 2 ().

For any 2n, 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 (𝕋 2 ,λ 2 ), where 𝔽 n is seen as a subgroup of SL 2 ().

DOI : 10.24033/asens.2106
Classification : 37A20, 46L10
Keywords: free groups, orbit equivalence
Mot clés : groupes libres, équivalence orbitale
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Ioana, Adrian. Non-orbit equivalent actions of $\mathbb {F}_n$. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 4, pp. 675-696. doi : 10.24033/asens.2106. http://www.numdam.org/articles/10.24033/asens.2106/

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