Measurable bounded cohomology of measured groupoids

Autor:	Sarti, Filippo, Savini, Alessio
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems Mathematics - Functional Analysis Mathematics - Group Theory 22D40 28D05 20J06
Druh dokumentu:	Working Paper
Popis:	We introduce the notion of measurable bounded cohomology for measured groupoids, extending continuous bounded cohomology of locally compact groups. We show that the measurable bounded cohomology of the semidirect groupoid associated to a measure class preserving action of a locally compact group $G$ on a regular space is isomorphic to the continuous bounded cohomology of $G$ with twisted coefficients. We also prove the invariance of measurable bounded cohomology under similarity. As an application, we compare the bounded cohomology of (weakly) orbit equivalent actions and of measure equivalent groups. In this way we recover an isomorphism in bounded cohomology similar to one proved by Monod and Shalom. For amenable groupoids, we show that the measurable bounded cohomology vanishes. This generalizes previous results by Monod, Anantharaman-Delaroche and Renault, and Blank. Comment: 48 pages. Comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.07765 Zobrazit plný text záznamu View this record from Arxiv