Hard Legendrian unknots

Joseph Breen; Austin Christian; Angela Wu

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arXiv · 2604.27213

Hard Legendrian unknots

Joseph Breen·Austin Christian·Angela Wu

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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.

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Joseph Breen, Austin Christian, Angela Wu. 2026-04-29. Hard Legendrian unknots. https://arxiv.org/abs/2604.27213

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