# The geometry of the disk complex

@article{Masur2010TheGO, title={The geometry of the disk complex}, author={Howard A. Masur and Saul Schleimer}, journal={Journal of the American Mathematical Society}, year={2010}, volume={26}, pages={1-62} }

We give a distance estimate for the disk complex. We use the distance estimate to prove that the disk complex is Gromov hyperbolic. As another application of our techniques, we find an algorithm which computes the Hempel distance of a Heegaard splitting, up to an error depending only on the genus.

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