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On Tunnel Number One Knots that are not (1,n)
Student-Run Geometry/Topology Seminar| Speaker: | George Mossessian, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Dec 5 2012, 4:10PM |
The tunnel number of a knot K is the minimal number of arcs that must be properly embedded in the closure of the complement of K so that the complement of K union the arcs is a handlebody. We will show that the bridge number of a t-bridge knot in S3 with respect to an unknotted genus t surface is bounded below by a function of the distance of the Heegaard splitting induced by the t brides. It folows that for any natural number n, there is a tunnel number one knot in S3 that is not (1,n). This talk is an exposition of the paper of the same name by Abigail Thompson and Jesse Johnson, 2007, arXiv:math/0606226.