We study cocycles of countable groups Γ 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 Γ 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.
Sergey I. Bezuglyi; Shrey Sanadhya. Cohomology of hyperfinite Borel actions. Groups, geometry, and dynamics, Tome 15 (2021) no. 4, pp. 1363-1398. doi: 10.4171/ggd/633
@article{10_4171_ggd_633,
author = {Sergey I. Bezuglyi and Shrey Sanadhya},
title = {Cohomology of hyperfinite {Borel} actions},
journal = {Groups, geometry, and dynamics},
pages = {1363--1398},
year = {2021},
volume = {15},
number = {4},
doi = {10.4171/ggd/633},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/633/}
}
TY - JOUR
AU - Sergey I. Bezuglyi
AU - Shrey Sanadhya
TI - Cohomology of hyperfinite Borel actions
JO - Groups, geometry, and dynamics
PY - 2021
SP - 1363
EP - 1398
VL - 15
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/633/
DO - 10.4171/ggd/633
ID - 10_4171_ggd_633
ER -
