Algebraic & Geometric Topology

An algorithm for finding parameters of tunnels

Kai Ishihara

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Abstract

Cho and McCullough gave a numerical parameterization of the collection of all tunnels of all tunnel number 1 knots and links in the 3–sphere. Here we give an algorithm for finding the parameter of a given tunnel by using its Heegaard diagram.

Article information

Source
Algebr. Geom. Topol., Volume 11, Number 4 (2011), 2167-2190.

Dates
Received: 17 November 2009
Revised: 17 May 2011
Accepted: 30 May 2011
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715265

Digital Object Identifier
doi:10.2140/agt.2011.11.2167

Mathematical Reviews number (MathSciNet)
MR2826935

Zentralblatt MATH identifier
1232.57010

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx]

Keywords
unknotting tunnel Heegaard diagram parameter of tunnel

Citation

Ishihara, Kai. An algorithm for finding parameters of tunnels. Algebr. Geom. Topol. 11 (2011), no. 4, 2167--2190. doi:10.2140/agt.2011.11.2167. https://projecteuclid.org/euclid.agt/1513715265


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References

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