The structure of relatively hyperbolic groups in convex real projective geometry

We prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex cocompactly on properly convex domains in real projective space.We also establish a characterization of such groups in terms of the existence of an invariant collection of closed unbounded convex subsets with good isolation properties.This is a real projective analogue of results of Hindawi-Hruska-Kleiner for CAT.0/ spaces.We also obtain an equivariant homeomorphism between the Bowditch boundary of the group and a quotient of the ideal boundary.20F65, 20F67, 22E40, 57N16, 57S20