Cohomology of hyperfinite Borel actions

Sergey Bezuglyi; Shrey Sanadhya

doi:10.4171/GGD/633

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Cohomology of hyperfinite Borel actions

Sergey Bezuglyi and Shrey Sanadhya

Groups, geometry and dynamics, Vol.15(4), pp.1363-1398

01/01/2021

DOI: 10.4171/GGD/633

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Abstract

We study cocycles of countable groups F of Borel automorphisms of a standard Borel space (X, B) taking values in a locally compact second countable group G. We prove that for a hyperfinite group F the subgroup of coboundaries is dense in the group of cocycles. We describe all Borel cocycles of the 2-odometer and show that any such cocycle is cohomologous to a cocycle with values in a countable dense subgroup H of G. We also provide a Borel version of Gottschalk-Hedlund theorem.

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Details

Title: Subtitle: Cohomology of hyperfinite Borel actions
Creators: Sergey Bezuglyi - University of Iowa
Shrey Sanadhya - University of Iowa
Resource Type: Journal article
Publication Details: Groups, geometry and dynamics, Vol.15(4), pp.1363-1398
DOI: 10.4171/GGD/633
ISSN: 1661-7207
eISSN: 1661-7215
Publisher: EUROPEAN MATHEMATICAL SOC-EMS
Number of pages: 36
Language: English
Date published: 01/01/2021
Academic Unit: Mathematics
Record Identifier: 9984241039802771

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