Convex cocompact actions in real projective geometry

By J. Danciger, Franccois Gu'eritaud, Fanny Kassel. Annales Scientifiques de l'Ecole Normale Supérieure, 2017

67 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5a5ada334ad05e86394ebac356e02ec99a6916c7