Cohomology of hyperfinite Borel actions
Sergey I. Bezuglyi
University of Iowa, Iowa City, USAShrey Sanadhya
University of Iowa, Iowa City, USA
![Cohomology of hyperfinite Borel actions cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-15-issue-4.png&w=3840&q=90)
Abstract
We study cocycles of countable groups of Borel automorphisms of a standard Borel space taking values in a locally compact second countable group . We prove that for a hyperfinite group the subgroup of coboundaries is dense in the group of cocycles. We describe all Borel cocycles of the -odometer and show that any such cocycle is cohomologous to a cocycle with values in a countable dense subgroup of . We also provide a Borel version of Gottschalk–Hedlund theorem.
Cite this article
Sergey I. Bezuglyi, Shrey Sanadhya, Cohomology of hyperfinite Borel actions. Groups Geom. Dyn. 15 (2021), no. 4, pp. 1363–1398
DOI 10.4171/GGD/633