#### Volume 19, issue 4 (2015)

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Projective deformations of weakly orderable hyperbolic Coxeter orbifolds

### Suhyoung Choi and Gye-Seon Lee

Geometry & Topology 19 (2015) 1777–1828
##### 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 $\mathfrak{2}m$ generated by two reflections. For $n\ge \mathfrak{3}$, we study the deformation space of real projective structures on a compact Coxeter $n$–orbifold $Q$ admitting a hyperbolic structure. Let ${e}_{+}\left(Q\right)$ be the number of ridges of order greater than or equal to $\mathfrak{3}$. A neighborhood of the hyperbolic structure in the deformation space is a cell of dimension ${e}_{+}\left(Q\right)-n$ if $n=\mathfrak{3}$ and $Q$ is weakly orderable, ie the faces of $Q$ can be ordered so that each face contains at most $\mathfrak{3}$ edges of order $\mathfrak{2}$ in faces of higher indices, or $Q$ is based on a truncation polytope.

##### Keywords
real projective structure, orbifold, moduli space, Coxeter groups, representations of groups
##### Mathematical Subject Classification 2010
Primary: 57M50, 57N16
Secondary: 53A20, 53C15