Algebraic & Geometric Topology

Stabilizing Heegaard splittings of high-distance knots

George Mossessian

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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.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 6 (2016), 3419-3443.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841265

Digital Object Identifier
doi:10.2140/agt.2016.16.3419

Mathematical Reviews number (MathSciNet)
MR3584263

Zentralblatt MATH identifier
06666105

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

Keywords
knot complement high distance common stabilization Heegaard splitting tunnel system

Citation

Mossessian, George. Stabilizing Heegaard splittings of high-distance knots. Algebr. Geom. Topol. 16 (2016), no. 6, 3419--3443. doi:10.2140/agt.2016.16.3419. https://projecteuclid.org/euclid.agt/1510841265


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