#### Volume 9, issue 1 (2009)

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Cabling sequences of tunnels of torus knots

### Sangbum Cho and Darryl McCullough

Algebraic & Geometric Topology 9 (2009) 1–20
##### Abstract

In previous work, we developed a theory of tunnels of tunnel number $1$ knots in ${S}^{3}$. 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

##### Keywords
knot, link, tunnel, torus knot
Primary: 57M25
##### Publication
Received: 5 August 2008
Revised: 22 October 2008
Accepted: 11 December 2008
Published: 5 January 2009
##### Authors
 Sangbum Cho University of California at Riverside Department of Mathematics Riverside California 92521 USA Darryl McCullough University of Oklahoma Department of Mathematics Norman Oklahoma 73019-3103 USA http://www.math.ou.edu/~dmccullough/