Oberwolfach Seminar: Applications of Teichmüller Theory to 3-Manifolds

Date:
May 27th - June 2nd, 2007
Organizers:
Ursula Hamenstädt, Bonn
Cyril Lecuri, Toulouse
Jean-Pierre Otal, Toulouse
Programme/Report:

The goal of the seminar was to introduce recent results on the geometry of Teichmueller space and their applications to the structure of hyperbolic 3-manifolds.

1. The so-called ending lamination conjecture in full generality states that a hyperbolic 3-manifold with finitely generated fundamental group is topologically tame and up to isometry determined by the topology compact core and by the ending invariants. This conjecture was proved in various parts during the first 5 years of this century.
A special case of the conjecture is the case that the hyperbolic manifold is homeormorphic to the product of a surface with the real line and that its injectivity radius is bounded from below by a positive constant. In this case the conjecture was established in 1994 by Minsky. In the seminar, a complete proof of this including all background material was presented using the curve graph as the main (recent) tool.

2. The Weil-Petersen geometry of Teichmueller space was presented using a new approach due to Glutsyuk which is much more elementary than the classical approach of Ahlfors.

3. A recent result of Brock relates in a direct way the volume of the convex core of a hyperbolic 3-manifold diffeomorphic to a the product of a surface with the real line to the Weil-Petersen distance of the boundary surfaces of its convex core. This result highlights the connection between the geometry of the convex core of such a manifold and the Weil-Petersen geometry in the absense of injectivity radius bounds.

The material presented in the seminar will appear as a Birkhaeuser Oberwolfach Seminar volume.

Prerequisites/Literature:
Will be announced at the seminar.
Deadline for applications:
April 1, 2007

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. The Institute covers accommodation and food. Travel expenses cannot be reimbursed. Applications including

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.


Mathematisches Forschungsinstitut Oberwolfach   updated: February 15, 2008