Geometry & Topology
- Geom. Topol.
- Volume 19, Number 4 (2015), 1777-1828.
Projective deformations of weakly orderable hyperbolic Coxeter orbifolds
A Coxeter –orbifold is an –dimensional orbifold based on a polytope with silvered boundary facets. Each pair of adjacent facets meet on a ridge of some order , whose neighborhood is locally modeled on modulo the dihedral group of order generated by two reflections. For , we study the deformation space of real projective structures on a compact Coxeter –orbifold admitting a hyperbolic structure. Let be the number of ridges of order greater than or equal to . A neighborhood of the hyperbolic structure in the deformation space is a cell of dimension if and is weakly orderable, ie the faces of can be ordered so that each face contains at most edges of order in faces of higher indices, or is based on a truncation polytope.
Geom. Topol., Volume 19, Number 4 (2015), 1777-1828.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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.)
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