2017/05/27 by Danijela Damjanović, Disheng Xu, Damjanovic, Danijela +1 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1705.09857
openalex publication_date 2017/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that every smooth diffeomorphism group valued cocycle over certain abelian Anosov actions on tori (and more generally on infranilmanifolds), is a smooth coboundary on a finite cover, if the cocycle is center bunched and trivial at a fixed point. For smooth cocycles which are not trivial at a fixed point, we have smooth reduction of cocycles to constant ones, when lifted to the universal cover. These results on cocycle trivialisation apply, via the existing global rigidity results, to maximal Cartan actions by Anosov diffeomorphisms (with at least one transitive), on any compact smooth manifold. This is the first rigidity result for cocycles over higher rank abelian actions, with values in diffeomorphism groups, which does not require any restrictions on the smallness of the cocycle, nor on the diffeomorphism group.