Algebraic & Geometric Topology

Cabling sequences of tunnels of torus knots

Sangbum Cho and Darryl McCullough

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In previous work, we developed a theory of tunnels of tunnel number 1 knots in S3. It yields a parameterization in which each tunnel is described uniquely by a finite sequence of rational parameters and a finite sequence of 0s and 1s, that together encode a procedure for constructing the knot and tunnel. In this paper we calculate these invariants for all tunnels of torus knots

Article information

Algebr. Geom. Topol., Volume 9, Number 1 (2009), 1-20.

Received: 5 August 2008
Revised: 22 October 2008
Accepted: 11 December 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

knot link tunnel torus knot


Cho, Sangbum; McCullough, Darryl. Cabling sequences of tunnels of torus knots. Algebr. Geom. Topol. 9 (2009), no. 1, 1--20. doi:10.2140/agt.2009.9.1.

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