# Rigidity and flexibility of hyperbolic cone-3-manifolds and polyhedra

Hartmut Weiss
(LMU München)
Colloquium
Thursday, 4 April, 2013, at 15:30-16:30, in 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 $2\pi$. These in particular imply a local version of Stoker's conjecture.
Organised by: QGM
Contact person: Jørgen Ellegaard Andersen