Geometric Topology of Knots

The geometry of unknotting tunnels.

speaker: Jessica Purcell (Brigham Young University)

abstract: An unknotting tunnel is an arc in a 3-manifold M with torus boundary, such that the complement of the tunnel in M is a handlebody. Classically, one can "unknot" a knot or link by pulling its diagram along an unknotting tunnel. In 1995, Adams, and Sakuma and Weeks, asked three questions concerning the geometry of unknotting tunnels in a hyperbolic 3-manifold: Are they geodesic? Do they have bounded length? Are they canonical? While the answer to the first question is still open, we will describe fairly complete answers to all three questions in the case where M is created by a "generic" Dehn filling. As an application, there is an explicit family of knots in the 3-sphere whose tunnels are arbitrarily long. This is joint with Daryl Cooper and David Futer.

timetable:
Thu 26 May, 10:00 - 10:45, Aula Dini
<< Go back