Comptes Rendus
no. 9
Functional analysis/Dynamical systems
On sofic groupoids and their full groups
[Sur les groupoïdes sofiques et leurs groupes pleins]

Présenté par : Étienne Ghys

Luiz Cordeiro1
1 University of Ottawa, Canada
Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 957-962.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.07.003
Luiz Cordeiro 1

1 University of Ottawa, Canada 
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     language = {en},
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Luiz Cordeiro. On sofic groupoids and their full groups. Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 957-962. doi : 10.1016/j.crma.2018.07.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.07.003/

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