An algorithm for finding parameters of tunnels
Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 2167-2190
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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.

DOI : 10.2140/agt.2011.11.2167
Keywords: unknotting tunnel, Heegaard diagram, parameter of tunnel

Ishihara, Kai  1

1 Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
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Ishihara, Kai. An algorithm for finding parameters of tunnels. Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 2167-2190. doi: 10.2140/agt.2011.11.2167

[1] J Berge, Embedding the exteriors of one-tunnel knots and links in the $3$–sphere, unpublished manuscript

[2] S Cho, D Mccullough, Cabling sequences of tunnels of torus knots, Algebr. Geom. Topol. 9 (2009) 1

[3] S Cho, D Mccullough, The tree of knot tunnels, Geom. Topol. 13 (2009) 769

[4] S Cho, D Mccullough, Tunnel leveling, depth, and bridge numbers, Trans. Amer. Math. Soc. 363 (2011) 259

[5] A T Fomenko, S V Matveev, Algorithmic and computer methods for three-manifolds, Math. and its Appl. 425, Kluwer (1997)

[6] H Goda, C Hayashi, Genus two Heegaard splittings of exteriors of $1$–genus $1$–bridge knots, preliminary version

[7] H Goda, C Hayashi, Genus two Heegaard splittings of exteriors of $1$–genus $1$–bridge knots

[8] C M Gordon, J Luecke, Knots are determined by their complements, Bull. Amer. Math. Soc. $($N.S.$)$ 20 (1989) 83

[9] T Homma, M Ochiai, M O Takahashi, An algorithm for recognizing $S^{3}$ in $3$–manifolds with Heegaard splittings of genus two, Osaka J. Math. 17 (1980) 625

[10] K Morimoto, M Sakuma, On unknotting tunnels for knots, Math. Ann. 289 (1991) 143

[11] M Ochiai, Heegaard diagrams and Whitehead graphs, Math. Sem. Notes Kobe Univ. 7 (1979) 573

[12] M Scharlemann, A Thompson, Unknotting tunnels and Seifert surfaces, Proc. London Math. Soc. $(3)$ 87 (2003) 523

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