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 ${\mathbb{Z}}^{d-2}$, 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.

45 pages, 12 figures, 10 tables

References in corpus (1)

• Exotic torus manifolds and equivariant smooth structures on quasitoric manifolds

Cited by in corpus (1)

• Convex co-compact groups with one dimensional boundary faces