Cabling sequences of tunnels of torus knots

Details Cabling sequences of tunnels of torus knots Cabling sequences of tunnels of torus knots

2008-12-07

arxiv.org/abs/0812.1389v1

Mathematics

Geometric Topology

17 pages, 12 figures, to appear in Algebraic and Geometric Topology

Scientific paper

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.

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