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Local rigidity of higher rank partially hyperbolic algebraic actions (1103.3077v2)

Published 16 Mar 2011 in math.DS

Abstract: We give a complete solution to the local classification program of higher rank partially hyperbolic algebraic actions. We show $C\infty$ 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.

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