Divisible convex sets with properly embedded cones

Abstract

In this article we construct many examples of properly convex irreducible domains divided by Zariski dense relatively hyperbolic groups in every dimension at least 3. This answers a question of Benoist. Relative hyperbolicity and non-strict convexity are captured by a family of properly embedded cones (convex hulls of points and ellipsoids) in the domain. Our construction is most flexible in dimension 3 where we give a purely topological criterion for the existence of a large deformation space of geometrically controlled convex projective structures with totally geodesic boundary on a compact 3-manifold.

arXiv comment90 pages. Comments are welcome!

References in corpus (10)

• Introduction to Arithmetic Groups
• Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces
• Convex projective structures on Gromov--Thurston manifolds
• A Geometric transition from hyperbolic to anti de Sitter geometry
• Convex projective structures on non-hyperbolic three-manifolds
• Collisions of particles in locally AdS spacetimes I. Local description and global examples
• Generalized Cusps in Real Projective Manifolds: Classification
• A higher rank rigidity theorem for convex real projective manifolds
• Convex projective manifolds with a cusp of any non-diagonalizable type
• A small closed convex projective 4-manifold via Dehn filling