Cabling sequences of tunnels of torus knots
Geometric Topology
2014-10-01 v1
Abstract
This is the second of three papers that refine and extend portions of our earlier preprint, "The depth of a knot tunnel." Together, they rework the entire preprint. The theory of tunnel number 1 knots that we introduced in "The tree of knot tunnels" 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
Cite
@article{arxiv.0812.1389,
title = {Cabling sequences of tunnels of torus knots},
author = {Sangbum Cho and Darryl McCullough},
journal= {arXiv preprint arXiv:0812.1389},
year = {2014}
}
Comments
17 pages, 12 figures, to appear in Algebraic and Geometric Topology