English

Genus one cobordisms between torus knots

Geometric Topology 2020-06-25 v3

Abstract

We determine the pairs of torus knots that have a genus one cobordism between them, with one notable exception. This is done by combining obstructions using ν+\nu^+ from the Heegaard Floer knot complex and explicit constructions of cobordisms. As an application, we determine the pairs of torus knots related by a single crossing change. Also, we determine the pairs of Thurston-Bennequin number maximizing Legendrian torus knots that have a genus one exact Lagrangian cobordism, with one exception.

Keywords

Cite

@article{arxiv.1910.01672,
  title  = {Genus one cobordisms between torus knots},
  author = {Peter Feller and JungHwan Park},
  journal= {arXiv preprint arXiv:1910.01672},
  year   = {2020}
}

Comments

20 pages, 12 figures. V3: Minor corrections and implementation of referee's recommendations. This version has been accepted for publication by IMRN

R2 v1 2026-06-23T11:34:07.232Z