Geometry, Topology and Dynamics Seminar
Jason DeBlois
UIC
Small-volume hyperbolic 3-manifolds with totally geodesic boundary
Abstract: A compact, orientable hyperbolic 3-manifold with totally geodesic boundary has volume at least 7.25 or it contains a "doubly
trimonic" submanifold. (For context, the smallest compact hyperbolic 3-manifolds with totally geodesic boundary have volume
approximately 6.45, and experimental results suggest that the second- and third-lowest volumes are roughly 7.1 and 7.33.) I will
say what a doubly trimonic 3-manifold is, describe some consequences of the result above, and sketch its proof. This relies on
and extends previous joint work with Peter Shalen.
Wednesday April 21, 2010 at 3:00 PM in SEO 612