Geometry & Topology

Projective deformations of weakly orderable hyperbolic Coxeter orbifolds

Suhyoung Choi and Gye-Seon Lee

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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 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.

Article information

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

Dates
Received: 16 July 2012
Revised: 23 July 2014
Accepted: 16 September 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds 57N16: Geometric structures on manifolds [See also 57M50]
Secondary: 53A20: Projective differential geometry 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
real projective structure orbifold moduli space Coxeter groups representations of groups

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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