Algebraic & Geometric Topology

Cabling sequences of tunnels of torus knots

Abstract

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 $0$s and $1$s, 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

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

Dates
Revised: 22 October 2008
Accepted: 11 December 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796954

Digital Object Identifier
doi:10.2140/agt.2009.9.1

Mathematical Reviews number (MathSciNet)
MR2471129

Zentralblatt MATH identifier
1170.57005

Keywords

Citation

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. https://projecteuclid.org/euclid.agt/1513796954

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