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.
- full name and address, including e-mail address
- present position, university
- name of supervisor of Ph.D. thesis
- a short summary of previous work and interest
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
.