Hard Legendrian unknots
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910177955938304 |
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| author | Breen, Joseph Christian, Austin Wu, Angela |
| author_facet | Breen, Joseph Christian, Austin Wu, Angela |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27213 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hard Legendrian unknots Breen, Joseph Christian, Austin Wu, Angela Geometric Topology Symplectic Geometry 57K33 (Primary) 57K10 (Secondary) 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. |
| title | Hard Legendrian unknots |
| topic | Geometric Topology Symplectic Geometry 57K33 (Primary) 57K10 (Secondary) |
| url | https://arxiv.org/abs/2604.27213 |