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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The geometry of the disk complex


Authors: Howard Masur and Saul Schleimer
Journal: J. Amer. Math. Soc. 26 (2013), 1-62
MSC (2010): Primary 57M50
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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Additional Information

Howard Masur
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: masur@math.uic.edu

Saul Schleimer
Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
Email: s.schleimer@warwick.ac.uk

DOI: http://dx.doi.org/10.1090/S0894-0347-2012-00742-5
PII: S 0894-0347(2012)00742-5
Received by editor(s): November 23, 2010
Received by editor(s) in revised form: April 6, 2012
Published electronically: August 22, 2012
Additional Notes: This work is in the public domain.