Title: Rigidity and flexibility of hyperbolic cone-3-manifolds and polyhedra
2013.03.20 |
| Date | Thu 04 Apr |
| Time | 15:30 — 16:30 |
| Location | Aud. G1 (1532-116) |
Abstract: Stoker's conjecture asks if a convex polyhedron in hyperbolic 3-space is determined up to a rigid motion by its combinatorics and its dihedral angles. A similar question can be asked for hyperbolic cone-3-manifolds. A hyperbolic cone-manifold is a 3-manifold equipped with a singular hyperbolic structure that has edge-type singularities along an embedded graph. Examples are provided by doubles of polyhedra or hyperbolic 3-orbifolds. Historically, cone-manifolds had been introduced by Thurston as a tool to geometrize 3-orbifolds. I will discuss recent results, partially obtained in joint work with G. Montcouquiol, concerning the local rigidity of hyperbolic cone-3-manifolds with cone-angles less than 2?. These in particular imply a local version of Stoker's conjecture.
