Volume 14, issue 2 (2014)

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Gordian adjacency for torus knots

Peter Feller

Algebraic & Geometric Topology 14 (2014) 769–793
Abstract

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 × . 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.

Keywords
Gordian distance, unknotting number, torus knots, plane curve singularities, adjacency
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 14B07
References
Publication
Received: 21 March 2013
Revised: 21 August 2013
Accepted: 22 August 2013
Published: 30 January 2014
Authors
Peter Feller
Universität Bern
Sidlerstrasse 5
CH-3012
Bern
Switzerland