## Geometry & Topology

### 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 $ℝn$ modulo the dihedral group of order $2m$ 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.

#### Article information

Source
Geom. Topol., Volume 19, Number 4 (2015), 1777-1828.

Dates
Revised: 23 July 2014
Accepted: 16 September 2014
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510858796

Digital Object Identifier
doi:10.2140/gt.2015.19.1777

Mathematical Reviews number (MathSciNet)
MR3375519

Zentralblatt MATH identifier
1333.57028

#### Citation

Choi, Suhyoung; Lee, Gye-Seon. Projective deformations of weakly orderable hyperbolic Coxeter orbifolds. Geom. Topol. 19 (2015), no. 4, 1777--1828. doi:10.2140/gt.2015.19.1777. https://projecteuclid.org/euclid.gt/1510858796

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