Mathematics Colloquia and Seminars

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I will show that the complement in S3 of an n-bridge knot with bridge distance greater than 2n has at most 2n-choose-n minimal genus Heegaard splittings, any two of which are either isotopic, become isotopic after one stabilization, or become isotopic after min(2n-1, d(K)/2) stabilizations. I will show how to use these splittings to construct the set of minimal tunnel systems for such a knot, and indicate future questions concerning these knots that I will be working on.