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Common stabilizations for genus-two Heegaard splittings of non-simple tunnel-number-one knot exteriors
Student-Run Geometry/Topology Seminar| Speaker: | Kevin Lamb, UC Davis |
| Location: | TBA |
| Start time: | Thu, Apr 13 2017, 11:00AM |
Unknotting tunnels for knots in S^3 are in one-to-one correspondence with (closed-surface) genus-two Heegaard splittings of the knot's exterior. We study the Stabilization Problem for these splittings in the case where the knot exterior contains an essential torus. Such knots are called non-simple, and work by Morimoto-Sakuma classifies them and their unknotting tunnels. I will present work by Hagiwara that shows that all genus-two Heegaard splittings of these knot exteriors become isotopic after one stabilization.