Gordian adjacency for torus knots

Feller, Peter¹

¹Universität Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland

Algebraic and Geometric Topology, Tome 14 (2014) no. 2, pp. 769-793

Résumé

A knot K1 is called Gordian adjacent to a knot K2 if there exists an unknotting sequence for K2 containing K1. We provide a sufficient condition for Gordian adjacency of torus knots via the study of knots in the thickened torus S1 × S1 × ℝ. We also completely describe Gordian adjacency for torus knots of index 2 and 3 using Levine–Tristram signatures as obstructions to Gordian adjacency. Our study of Gordian adjacency is motivated by the concept of adjacency for plane curve singularities. In the last section we compare these two notions of adjacency.

Détail

DOI : 10.2140/agt.2014.14.769

Classification : 57M27, 14B07
Keywords: Gordian distance, unknotting number, torus knots, plane curve singularities, adjacency

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