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An algorithm for finding parameters of tunnels

Kai Ishihara
Algebraic & Geometric Topology 11 (2011) 2167–2190
DOI: 10.2140/agt.2011.11.2167
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.

Keywords
unknotting tunnel, Heegaard diagram, parameter of tunnel
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57N10
References
Publication
Received: 17 November 2009
Revised: 17 May 2011
Accepted: 30 May 2011
Published: 29 July 2011
Authors
Kai Ishihara
Department of Mathematics
Imperial College London
London
SW7 2AZ
UK