## Algebraic & Geometric Topology

### High distance knots

#### 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
Accepted: 22 March 2007
First available in Project Euclid: 20 December 2017

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

#### 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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