An Extension of the $sl(n)$ Polynomial to Knotted 4-Valent Graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917238198501376 |
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| author | Caprau, Carmen Wiest, Victoria |
| author_facet | Caprau, Carmen Wiest, Victoria |
| contents | We use planar 4-valent graphs and a graphical calculus involving such graphs to construct an invariant for balanced-oriented, knotted 4-valent graphs. Our invariant is an extension of the $sl(n)$ polynomial for classical knots and links. We also provide a minimal generating set of Reidemeister-type moves for diagrams of balanced-oriented, knotted 4-valent graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18144 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Extension of the $sl(n)$ Polynomial to Knotted 4-Valent Graphs Caprau, Carmen Wiest, Victoria Geometric Topology 57K12, 57K14 We use planar 4-valent graphs and a graphical calculus involving such graphs to construct an invariant for balanced-oriented, knotted 4-valent graphs. Our invariant is an extension of the $sl(n)$ polynomial for classical knots and links. We also provide a minimal generating set of Reidemeister-type moves for diagrams of balanced-oriented, knotted 4-valent graphs. |
| title | An Extension of the $sl(n)$ Polynomial to Knotted 4-Valent Graphs |
| topic | Geometric Topology 57K12, 57K14 |
| url | https://arxiv.org/abs/2601.18144 |