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Projective deformations of weakly orderable hyperbolic Coxeter orbifolds

Suhyoung Choi and Gye-Seon Lee

Geometry & Topology 19 (2015) 1777–1828

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 n 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.

real projective structure, orbifold, moduli space, Coxeter groups, representations of groups
Mathematical Subject Classification 2010
Primary: 57M50, 57N16
Secondary: 53A20, 53C15
Received: 16 July 2012
Revised: 23 July 2014
Accepted: 16 September 2014
Published: 29 July 2015
Proposed: Walter Neumann
Seconded: Benson Farb, Danny Calegari
Suhyoung Choi
Department of Mathematical Sciences
Daejeon 305-701
South Korea
Gye-Seon Lee
Mathematisches Institut
Ruprecht-Karls-Universität Heidelberg
D-69120 Heidelberg