Hard Legendrian unknots
Geometric Topology
2026-05-01 v1 Symplectic Geometry
Abstract
We initiate the study of Reidemeister hardness of Legendrian unknot front projections. Using normal rulings, we obstruct several infinite families of hard unknot diagrams from being drawn with max-tb unknot fronts, along with 1.7 million of the 2.6 million hard unknot diagrams studied in \cite{applebaum2024unknottingnumberhardunknot}. We construct infinitely many smoothly hard max-tb unknot diagrams, and bound their minimum possible writhe. With respect to these bounds, our constructions are conjecturally sharp.
Cite
@article{arxiv.2604.27213,
title = {Hard Legendrian unknots},
author = {Joseph Breen and Austin Christian and Angela Wu},
journal= {arXiv preprint arXiv:2604.27213},
year = {2026}
}
Comments
30 pages + references, 42 figures. Comments welcome