Algebraic & Geometric Topology

Gordian adjacency for torus knots

Peter Feller

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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.

Article information

Algebr. Geom. Topol., Volume 14, Number 2 (2014), 769-793.

Received: 21 March 2013
Revised: 21 August 2013
Accepted: 22 August 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 14B07: Deformations of singularities [See also 14D15, 32S30]

Gordian distance unknotting number torus knots plane curve singularities adjacency


Feller, Peter. Gordian adjacency for torus knots. Algebr. Geom. Topol. 14 (2014), no. 2, 769--793. doi:10.2140/agt.2014.14.769.

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