CONVEX PROJECTIVE GENERALIZED DEHN FILLING

Abstract

For d = 4, 5, 6, we exhibit the first examples of complete finite volume hyperbolic d-manifolds M with cusps such that infinitely many d-orbifolds M-m obtained from M by generalized Dehn filling admit properly convex real projective structures. The orbifold fundamental groups of M-m are Gromov-hyperbolic relative to a collection of subgroups virtually isomorphic to Z(d-2) , hence the images of the developing maps of the projective structures on M-m are new examples of divisible properly convex domains of the projective d-space which are not strictly convex, in contrast to the previous examples of Benoist.