Algebraic & Geometric Topology

High distance knots

Yair N Minsky, Yoav Moriah, and Saul Schleimer

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Abstract

We construct knots in S3 with Heegaard splittings of arbitrarily high distance, in any genus. As an application, for any positive integers t and b we find a tunnel number t knot in the three-sphere which has no (t,b)–decomposition.

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 3 (2007), 1471-1483.

Dates
Received: 25 August 2006
Accepted: 22 March 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796749

Digital Object Identifier
doi:10.2140/agt.2007.7.1471

Mathematical Reviews number (MathSciNet)
MR2366166

Zentralblatt MATH identifier
1167.57002

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

Keywords
Heegaard distance tunnel number knot bridge position

Citation

Minsky, Yair N; Moriah, Yoav; Schleimer, Saul. High distance knots. Algebr. Geom. Topol. 7 (2007), no. 3, 1471--1483. doi:10.2140/agt.2007.7.1471. https://projecteuclid.org/euclid.agt/1513796749


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