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arXiv · 1301.5248

Gordian adjacency for torus knots

Peter Feller
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Abstract

A knot K is called Gordian adjacent to a knot L if there exists an unknotting sequence for L containing K. We provide a sufficient condition for Gordian adjacency of torus knots via the study of knots in the thickened torus. We also completely describe Gordian adjacency for torus knots of index 2 and 3 using Levine-Tristram signatures as obstructions to Gordian adjacency. Finally, Gordian adjacency for torus knots is compared to the notion of adjacency for plane curve singularities.

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BibTeXRIS

Peter Feller. 2014-10-01. Gordian adjacency for torus knots. https://doi.org/10.2140/agt.2014.14.769

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