2011/03/16 by Wang, Zhenqi Jenny
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1103.3077
openalex publication_date 2011/03/16 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28
We give a complete solution to the local classification program of higher rank partially hyperbolic algebraic actions. We show C^∞ local rigidity of abelian ergodic algebraic actions for symmetric space examples, twisted symmetric space examples and automorphisms on nilmanifolds. The method is a combination of representation theory, harmonic analysis and a KAM iteration. A striking feature of the method is no specific information from representation theory is needed. It is the first time local rigidity for non-accessible partially hyperbolic actions has ever been obtained other than torus examples. Even for Anosov actions, our results are new: it is the first time twisted spaces with non-abelian nilradical have been treated in the literature.