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Maggy Tomova (Rice University)

### Title

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

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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