Projective deformations of weakly orderable hyperbolic Coxeter orbifolds

Choi, Suhyoung¹ ; Lee, Gye-Seon²

¹ Department of Mathematical Sciences, KAIST, Daejeon 305-701, South Korea
² Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, D-69120 Heidelberg, Germany

Geometry & topology, Tome 19 (2015) no. 4, pp. 1777-1828.

Résumé

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.

Détail

DOI : 10.2140/gt.2015.19.1777

Classification : 57M50, 57N16, 53A20, 53C15
Keywords: real projective structure, orbifold, moduli space, Coxeter groups, representations of groups

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