Projective deformations of weakly orderable hyperbolic Coxeter orbifolds

Abstract

A Coxeter n-orbifold is an n-dimensional orbifold based on a polytope with silvered boundary facets. Each pair of adjacent facets meet on a ridge of some order m, whose neighborhood is locally modeled on R-n modulo the dihedral group of order 2 m generated by two reflections. For n >= 3, we study the deformation space of real projective structures on a compact Coxeter n-orbifold Q admitting a hyperbolic structure. Let e(+)(Q) be the number of ridges of order greater than or equal to 3. A neighborhood of the hyperbolic structure in the deformation space is a cell of dimension e(+)(Q) - n if n = 3 and Q is weakly orderable, ie the faces of Q can be ordered so that each face contains at most 3 edges of order 2 in faces of higher indices, or Q is based on a truncation polytope.