Title: Hyperbolicity from the viewpoint
of Heegaard splittings
Abstract: Our understanding of 3-manifolds and in particular hyperbolic
3-manifolds has advanced significantly in recent years. A very important
development is relating combinatorial data on 3-manifolds and the geometry
of the hyperbolic metric. Such an approach has been most successful in
describing the geometry of open hyperbolic 3-manifolds by starting from
the combinatorial data of the ends. We will show how similar pictures and
descriptions can be used to study the geometry of closed hyperbolic 3-manifolds.
In this case the combinatorial information is obtained from a Heegaard
splitting and is used to construct approximations of the hyperbolic metric.