3-manifolds, hyperbolic geometry and models
Hossein Namazi (University of Texas)

The proof of the Geometrization Conjecture by Perelman is a major development in our understanding of 3-manifolds. However there is a big difference between knowing the existence of a geometric structure and describing it. We will demonstrate that the mere existence of the geometric structure fails to answer many simple geometric and topological questions and why one needs a more effective proof which allows us to describe the geometry. We explain an approach to find such a description by starting from a Heegaard splitting or some other decompositions of a 3-manifold and use hyperbolic geometry technics which have been developed recently. We explain how this provides models for the geometries of a variety of examples and its new applications.

Colloquium, Department of Mathematics, Rice University
November 6, 2008, 4-5PM, HB 227

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