GROUP ACTIONS AND AUTOMORPHIC FORMS SEMINAR

3/8/2005

Boris Kalinin,
University of South Alabama

On smooth classification of Z^k and R^k Cartan actions

We consider actions of Z^k by hyperbolic diffeomorphisms of a compact manifold and R^k actions normally hyperbolic to the orbit foliation. Algebraic examples of such actions have been extensively studied recently. In contrast to Anosov diffeomorphisms and flows, the higher rank actions exhibit such remarkable properties as rigidity of invariant measures and rigidity of measure preserving isomorphisms. These algebraic actions are often locally rigid, i.e. smoothly conjugate to any small perturbation. We will discuss the problem of smooth classification of nonalgebraic actions, i.e. the existence of a smooth conjugacy to an algebraic model, and related rigidity questions. Our main result is a classification for certain classes of Cartan actions.