Cabling sequences of tunnels of torus knots

Cho, Sangbum; McCullough, Darryl

doi:10.2140/agt.2009.9.1

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Cabling sequences of tunnels of torus knots

Sangbum Cho and Darryl McCullough

Algebraic & Geometric Topology 9 (2009) 1–20

DOI: 10.2140/agt.2009.9.1

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

Mathematical Subject Classification 2000

Primary: 57M25

References

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/

Volume 9, issue 1 (2009)