The geometry of the disk complex

Masur, Howard; Schleimer, Saul

doi:10.1090/S0894-0347-2012-00742-5

The geometry of the disk complex
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by Howard Masur and Saul Schleimer

J. Amer. Math. Soc. 26 (2013), 1-62

DOI: https://doi.org/10.1090/S0894-0347-2012-00742-5

Published electronically: August 22, 2012

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Abstract:

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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