Cohomology of Dominated Diffeomorphism-Valued Cocycles Over Hyperbolic Systems

TL;DR

This paper proves a rigidity result for dominated Hölder cocycles valued in diffeomorphism groups over hyperbolic systems, showing that equal periodic data implies cohomology.

Contribution

It establishes a new rigidity theorem linking periodic data to cohomology for diffeomorphism-valued cocycles over hyperbolic systems.

Findings

Cocycles with equal periodic data are cohomologous.

Rigidity holds for dominated Hölder cocycles in diffeomorphism groups.

The result extends understanding of cocycle classification over hyperbolic systems.

Abstract

We prove a rigidity theorem for dominated H\"{o}lder cocycles with values on diffeomorphism groups of a compact manifold over hyperbolic homeomorphisms. More precisely, we show that if two such cocycles have equal periodic data, then they are cohomologous.