Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 2 (2014), 769-793.
Gordian adjacency for torus knots
A knot is called Gordian adjacent to a knot if there exists an unknotting sequence for containing . 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. 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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 14B07: Deformations of singularities [See also 14D15, 32S30]
Feller, Peter. Gordian adjacency for torus knots. Algebr. Geom. Topol. 14 (2014), no. 2, 769--793. doi:10.2140/agt.2014.14.769. https://projecteuclid.org/euclid.agt/1513715846