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2016 Stabilizing Heegaard splittings of high-distance knots
George Mossessian
Algebr. Geom. Topol. 16(6): 3419-3443 (2016). DOI: 10.2140/agt.2016.16.3419

Abstract

Suppose K is a knot in S3 with bridge number n and bridge distance greater than 2n. We show that there are at most 2n n distinct minimal-genus Heegaard splittings of S3 η(K). These splittings can be divided into two families. Two splittings from the same family become equivalent after at most one stabilization. If K has bridge distance at least 4n, then two splittings from different families become equivalent only after n 1 stabilizations. Furthermore, we construct representatives of the isotopy classes of the minimal tunnel systems for K corresponding to these Heegaard surfaces.

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George Mossessian. "Stabilizing Heegaard splittings of high-distance knots." Algebr. Geom. Topol. 16 (6) 3419 - 3443, 2016. https://doi.org/10.2140/agt.2016.16.3419

Information

Received: 8 September 2015; Revised: 15 February 2016; Accepted: 21 April 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 06666105
MathSciNet: MR3584263
Digital Object Identifier: 10.2140/agt.2016.16.3419

Subjects:
Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.16 • No. 6 • 2016
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