Geometry, Topology and Dynamics Seminar
Bell Foozwell
University of Melbourne
Haken n-manifolds
Abstract: We study Haken $n$-manifolds, which are manifolds defined by generalising
useful properties of Haken 3-manifolds to higher dimensions. In
particular, a Haken $n$-manifold has a hierarchy. This means that such a
manifold can be split open along a finite collection of essential,
embedded, codimension-one submanifolds, the end result being a collection
of $n$-cells. Foundational results concerning this class of manifolds
include a solution to the word problem, and the nature of the universal
covering spaces. We also study examples of Haken 4-manifolds, which
include certain surface bundles, and some hyperbolic examples.
Monday October 10, 2005 at 3:00 PM in SEO 512