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 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