Maggy Tomova (Rice University)


Bounds on the distance of a Heegaard splitting of a knot complement


Haken demonstrated that if a manifold M contains an essential sphere, every Heegaard splitting of M has distance 0. Hartshorn later showed that the genus of any essential surface similarly bounds the distance of a Heegaard splitting. Scharlemann and I showed that the distance is also bounded by the genus of any other Heegaard surface. Most recently I showed that if the manifold in question is a knot complement, the distance of any Heegaard splitting is bounded by the Euler characteristic of a bridge surface for the knot. I will briefly sketch the proof of this latest result and its uses.

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