Projective Anosov representations and convex cocompact actions

Andrew Zimmer (William & Mary)

In this talk we will describe two results which relate Anosov representations with convex cocompact actions on properly convex domains in real projective space. First, we will show that if a non-elementary word hyperbolic group is not commensurable to a non-trivial free product or the fundamental group of a closed hyperbolic surface, then then any irreducible projective Anosov representation of that group acts convex cocompactly on some properly convex domain in real projective space. Second, we will show that Anosov representations in general semisimple Lie groups can be defined in terms of the existence of a convex cocompact action on a properly convex domain in some real projective space (which depends on the semisimple Lie group and parabolic subgroup). Finally, we will give some applications.