Colloquium by Hartmut Weiss (LMU Munich)

Title: Rigidity and flexibility of hyperbolic cone-3-manifolds and polyhedra

2013.03.20 | Jane Jamshidi

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.