Seminar

Y. Benoist proved that if a closed three-manifold M admits a convex real projective structure, then M is topologically the union along tori of finitely many sub-manifolds each of which admits a complete finite volume hyperbolic structure on its interior. We describe some initial results in the direction of a potential converse to Benoist’s theorem. Specifically, we show that a cusped hyperbolic three-manifold may (under assumptions) be deformed to convex projective structures with totally geodesic torus boundary. Such structures may be (convexly) glued together whenever the geometry at the boundary matches up. In particular, we prove that many doubles of cusped hyperbolic three-manifolds admit convex projective structures. Joint work with Sam Ballas and Gye Seon Lee.