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Bridge Number and the Curve Complex
Geometry/Topology| Speaker: | Jesse Johnson, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Apr 19 2006, 4:10PM |
Description
An unknotting tunnel for a knot in the three-sphere determines a
simple closed curve in the standard genus-two Heegaard splitting of S^3.
This suggests a definition, via the curve complex, for the "distance" of the
unknotting tunnel. I will show how this distance is related to the Seifert
genus of the knot, the existence of alternate tunnels, and in particular the
bridge number of the knot. I will also describe how the geometry of the
curve complex can be used to prove the existence of knots with arbitrarily
high distance tunnels.