English

Gordian adjacency for torus knots

Geometric Topology 2017-10-13 v2

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.

Keywords

Cite

@article{arxiv.1301.5248,
  title  = {Gordian adjacency for torus knots},
  author = {Peter Feller},
  journal= {arXiv preprint arXiv:1301.5248},
  year   = {2017}
}

Comments

21 pages, 8 figures. Minor corrections and implementation of referee's recommendations

R2 v1 2026-06-21T23:13:37.515Z