Cohomology of hyperfinite Borel actions

Sergey Bezuglyi, Shrey Sanadhya

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1363-1398
Number of pages36
JournalGroups, Geometry, and Dynamics
Issue number4
StatePublished - 1 Jan 2021
Externally publishedYes


  • Borel automorphism
  • Coboundary
  • Cocycle
  • Hyperfinite countable Borel equivalence relation
  • Odometer

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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