A generalization of the Epstein-Penner construction to projective manifolds

Abstract

We extend the canonical cell decomposition due to Epstein and Penner of a hyperbolic manifold with cusps to the strictly convex setting. It follows that a sufficiently small deformation of the holonomy of a finite volume strictly convex real projective manifold is the holonomy of some nearby projective structure with radial ends, provided the holonomy of each cusp has a fixed point.