[Sur le problème de la classification des actions libres ergodiques de groupes discrets non moyennables]
Nous montrons que, pour tout groupe dénombrable discret et non moyennable Γ, les relations de conjugaison, d'équivalence orbitale, d'équivalence orbitale stable, d'équivalence de von Neumann et d'équivalence de von Neumann stable des actions libres ergodiques de Γ sur un espace borélien standard muni d'une mesure de probabilité sans atomes ne sont pas Borel. Cela répond à une question de Kechris.
We show that, for any countable discrete nonamenable group Γ, the relations of conjugacy, orbit equivalence, stable orbit equivalence, von Neumann equivalence, and stable von Neumann equivalence of free ergodic pmp actions of Γ on the standard atomless probability space are not Borel. This answers a question of Kechris.
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@article{CRMATH_2017__355_10_1037_0,
author = {Gardella, Eusebio and Lupini, Martino},
title = {On the classification problem of free ergodic actions of nonamenable groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {1037--1040},
publisher = {Elsevier},
volume = {355},
number = {10},
year = {2017},
doi = {10.1016/j.crma.2017.10.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.10.004/}
}
TY - JOUR AU - Gardella, Eusebio AU - Lupini, Martino TI - On the classification problem of free ergodic actions of nonamenable groups JO - Comptes Rendus. Mathématique PY - 2017 SP - 1037 EP - 1040 VL - 355 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.10.004/ DO - 10.1016/j.crma.2017.10.004 LA - en ID - CRMATH_2017__355_10_1037_0 ER -
%0 Journal Article %A Gardella, Eusebio %A Lupini, Martino %T On the classification problem of free ergodic actions of nonamenable groups %J Comptes Rendus. Mathématique %D 2017 %P 1037-1040 %V 355 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.10.004/ %R 10.1016/j.crma.2017.10.004 %G en %F CRMATH_2017__355_10_1037_0
Gardella, Eusebio; Lupini, Martino. On the classification problem of free ergodic actions of nonamenable groups. Comptes Rendus. Mathématique, Tome 355 (2017) no. 10, pp. 1037-1040. doi : 10.1016/j.crma.2017.10.004. http://www.numdam.org/articles/10.1016/j.crma.2017.10.004/
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