Smooth classification of Cartan actions of higher rank semisimple Lie groups and their lattices

Abstract

Let G be a connected semisimple Lie group without compact factors whose real rank is at least 2, and let Γ\subset G be an irreducible lattice. We provide a C^\infty classification for volume-preserving Cartan actions of Γand G. Also, if G has real rank at least 3, we provide a C^\infty classification for volume-preserving, multiplicity free, trellised, Anosov actions on compact manifolds.