On the quantum $\mathfrak{sl}_3$ invariant of positive links
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917361948295168 |
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| author | Harper, Matthew Kalfagianni, Efstratia |
| author_facet | Harper, Matthew Kalfagianni, Efstratia |
| contents | We use the skein theory of $\mathfrak{sl}_3$-webs to study the properties of the quantum $\mathfrak{sl}_3$-link polynomial of positive links. We give explicit formulae for the three leading terms of the polynomial on positive links in terms of diagrammatic quantities of their positive diagrams. We show that a positive link is fibered if and only the second coefficient of the polynomial is equal to one. We also show that the third coefficient provides obstructions to representing links by positive braids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the quantum $\mathfrak{sl}_3$ invariant of positive links Harper, Matthew Kalfagianni, Efstratia Geometric Topology Quantum Algebra 57K16 (primary), 57K14, 57K10 We use the skein theory of $\mathfrak{sl}_3$-webs to study the properties of the quantum $\mathfrak{sl}_3$-link polynomial of positive links. We give explicit formulae for the three leading terms of the polynomial on positive links in terms of diagrammatic quantities of their positive diagrams. We show that a positive link is fibered if and only the second coefficient of the polynomial is equal to one. We also show that the third coefficient provides obstructions to representing links by positive braids. |
| title | On the quantum $\mathfrak{sl}_3$ invariant of positive links |
| topic | Geometric Topology Quantum Algebra 57K16 (primary), 57K14, 57K10 |
| url | https://arxiv.org/abs/2508.15153 |