[Sur les groupoïdes sofiques et leurs groupes pleins]
Nous démontrons dans cette note que plusieurs constructions de théorie de la mesure préservent la classe des groupoïdes sofiques. En particulier, nous montrons qu'un sous-groupoïde virtuellement sofique est sofique. Nous répondons aussi à une question de Conley, Kechris et Tucker-Drob en démontrant que, pour qu'un groupoïde apériodique muni d'une mesure de probabilité invariante soit sofique, il est nécessaire et suffisant que son groupe plein soit métriquement sofique.
We prove that the class of sofic groupoids is stable under several measure-theoretic constructions. In particular, we show that virtually sofic groupoids are sofic. We answer a question of Conley, Kechris, and Tucker-Drob by proving that an aperiodic pmp groupoid is sofic if and only if its full group is metrically sofic.
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@article{CRMATH_2018__356_9_957_0,
author = {Cordeiro, Luiz},
title = {On sofic groupoids and their full groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {957--962},
publisher = {Elsevier},
volume = {356},
number = {9},
year = {2018},
doi = {10.1016/j.crma.2018.07.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.07.003/}
}
TY - JOUR AU - Cordeiro, Luiz TI - On sofic groupoids and their full groups JO - Comptes Rendus. Mathématique PY - 2018 SP - 957 EP - 962 VL - 356 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.07.003/ DO - 10.1016/j.crma.2018.07.003 LA - en ID - CRMATH_2018__356_9_957_0 ER -
Cordeiro, Luiz. On sofic groupoids and their full groups. Comptes Rendus. Mathématique, Tome 356 (2018) no. 9, pp. 957-962. doi : 10.1016/j.crma.2018.07.003. http://www.numdam.org/articles/10.1016/j.crma.2018.07.003/
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