Mathematics Colloquia and Seminars

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Thompson proved that if a knot K in S^3 is in thin position but not in bridge position then its complement contains an essential meridional planar surface (mps). Later on Wu gave a way to find such a surface: a thinnest mps in S^3\K is essential. This result implies that width is "additive" under connected sum of mp-small knots.

I will give the definitions of all these concepts and if time permits the proof of Wu's theorem.