Convex cocompact actions in real projective geometry

We study a notion of convex cocompactness for (not necessarily irreducible) discrete subgroups of the projective general linear group acting on real projective space, and give various characterizations. A convex cocompact group in this sense need not be word hyperbolic, but we show that it still has some of the good properties of classical convex cocompact subgroups in rank-one Lie groups. Extending our earlier work arXiv:1701.09136 from the context of projective orthogonal groups, we show that for word hyperbolic groups preserving a properly convex open set in projective space, the above general notion of convex cocompactness is equivalent to a stronger convex cocompactness condition studied by Crampon-Marquis, and also to the condition that the natural inclusion be a projective Anosov representation. We investigate examples.Comment: 77 pages, 6 figures. Added appendix. Removed section on Anosov right-angled reflection groups, which will appear as a separate pape

Anosov representations and proper actions

We establish several characterizations of Anosov representations of word hyperbolic groups into real reductive Lie groups, in terms of a Cartan projection or Lyapunov projection of the Lie group. Using a properness criterion of Benoist and Kobayashi, we derive applications to proper actions on homogeneous spaces of reductive groups.Comment: 73 pages, 4 figures; to appear in Geometry & Topolog