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 ⊂ G be an irreducible lattice. We provide a C ∞ classification for volume-preserving Cartan actions of an d G. Also, if G has real rank at least 3, we provide a C ∞ classification for volume-preserving, multiplicity free, trellised, Anosov actions on compact manifolds.