Abelian Livsic theorems for Anosov flows

Abstract

We give two short proofs of the abelian Livsič theorem of Gogolev and Rodriguez Hertz. We show that these proofs may be extended to give new abelian Livsic theorems for positive density sets of null-homologous orbits and for amenable covers.

17 pages. Revised version after peer review. To appear in the Bulletin of the London Mathematical Society