The geometry of the disk complex

Masur, Howard¹ ; Schleimer, Saul²

¹ Department of Mathematics, University of Chicago, Chicago, Illinois 60637
² Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

Journal of the American Mathematical Society, Tome 26 (2013) no. 1, pp. 1-62

Résumé

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.

Détail

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

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