An orientable hyperbolic n - manifold is isometric to the quotient of hyperbolic n - space Hn by a discrete torsion free subgroup Γ of the group of orientation - preserving isometries of Hn. The group Γ is said to have finite covolume if Hn/Γ has finite volume, and is said to be cocompact if Hn/Γ is compact.
Among hyperbolic manifolds, the ones originating with arithmetically defined groups Γ form a family of special interest. These arithmetic groups fall naturally into two classes. They can be distinguished by the compactness or non - compactness of the corresponding manifold Hn/Γ. In the latter case the arithmetically defined group Γ has finite covolume.
This subject is related in various ways with number theory, geometry and topology, and, in turn, there are close connections with the theory of automorphic forms. Our objects of concern may be viewed as a most prominent example in the theory of arithmetic groups and their corresponding locally symmetric spaces. Thus, this seminar may very well serve as an introduction to the fruitful interaction between geometric and arithmetic questions, methods and results in the realm of this theory. It is intended to cover the following topic areas where there have been a number of important recent developments:
In addition, there will be a few more advanced lectures on methods developed in the realm of the theory of automorphic forms which might help in understanding the specific case of arithmetically defined hyperbolic manifolds.
should be sent as hard copy or by e-mail (.ps or .pdf file) to:
Prof. Dr. Gert-Martin Greuel
67663 Kaiserslautern, Germany