Non-orbit equivalent actions of 𝔽 n
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 42 (2009) no. 4, p. 675-696

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 ().

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 ().

DOI : https://doi.org/10.24033/asens.2106
Classification:  37A20,  46L10
Keywords: free groups, orbit equivalence
@article{ASENS_2009_4_42_4_675_0,
     author = {Ioana, Adrian},
     title = {Non-orbit equivalent actions of $\mathbb {F}\_n$},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 42},
     number = {4},
     year = {2009},
     pages = {675-696},
     doi = {10.24033/asens.2106},
     zbl = {1185.37009},
     mrnumber = {2568879},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2009_4_42_4_675_0}
}
Ioana, Adrian. Non-orbit equivalent actions of $\mathbb {F}_n$. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 42 (2009) no. 4, pp. 675-696. doi : 10.24033/asens.2106. http://www.numdam.org/item/ASENS_2009_4_42_4_675_0/

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