Mathematics Colloquia and Seminars

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It is well known that every closed, orientable 3-manifold has a Heegaard splitting. The splitting surface is traditionally a closed surface. In the context of knots in the 3-sphere, it is possible to construct a foliation (generally with finitely many singular leaves) of the knots's complement via Seifert surfaces. This foliation can be used to construct a Heegaard splitting in which the splitting surfaces is compact and orientable but not closed (and is comprised of two connected components) - we call it a "circular Heegaard splitting". For this type of Heegaard splitting, joint work with Patrick Weed has produced a generalization of the notion of distance of a Heegaard splitting to this new class of Heegaard splitting, called the "circular distance"
In this talk, we show that it is possible to put an upper bound on the circular distance of any circular Heegaard splitting of a knot complement using a strongly irreducible Heegaard splitting.

Previously at 1:10pm.