Normal surfaces in cubed and Haken 3-manifolds
by Hyam Rubinstein
Abstract: This is a joint project with Iain Aitchison and Bus Jaco. The idea is
to look at the similarity between Haken 3-manifolds and 3-manifolds
withe cubings of non-positive curvature. The behaviour of normal
surfaces in these two classes of manifolds provides an interesting
comparison - in both cases, the aim is to obtain finiteness results
similar to the well known ones for minimal surfaces of bounded genus
in negatively curved 3-manifolds. One application is a quick proof of
Johannson's finiteness result for Heegaard splittings of bounded
genus in Haken 3-manifolds.
An interesting question is whether there might be a way of putting a polyhedral metric of non-positive curvature directly on atoroidal Haken 3-manifolds.
For More Information: Lawrence Reeves email: firstname.lastname@example.org