Functional analysis/Dynamical systems
On sofic groupoids and their full groups
Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 957-962.

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.

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.

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Published online:
DOI: 10.1016/j.crma.2018.07.003
Cordeiro, Luiz 1

1 University of Ottawa, Canada
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Cordeiro, Luiz. 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. http://www.numdam.org/articles/10.1016/j.crma.2018.07.003/

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