Cabling sequences of tunnels of torus knots

Sangbum Cho; Darryl McCullough

doi:10.2140/agt.2009.9.1

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arXiv · 0812.1389

Cabling sequences of tunnels of torus knots

Sangbum Cho·Darryl McCullough

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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.

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BibTeX RIS

Sangbum Cho, Darryl McCullough. 2008-12-07. Cabling sequences of tunnels of torus knots. https://doi.org/10.2140/agt.2009.9.1

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