Harer-Zagier formulas for families of twisted hyperbolic knots
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910996668350464 |
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| author | Petrou, Andreani Hikami, Shinobu |
| author_facet | Petrou, Andreani Hikami, Shinobu |
| contents | In an attempt to generalise knot matrix models for non-torus knots, which currently remains an open problem, we derived formulas for the Harer-Zagier transform of the HOMFLY-PT polynomial for some infinite families of twisted hyperbolic knots. Among them, we found a family of Pretzel knots for which the transform has a fully factorised form, while for the remaining families considered it consists of sums of factorised terms. Their zeros have a remarkable structure as the modulus of their product always equals unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05919 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Harer-Zagier formulas for families of twisted hyperbolic knots Petrou, Andreani Hikami, Shinobu Mathematical Physics In an attempt to generalise knot matrix models for non-torus knots, which currently remains an open problem, we derived formulas for the Harer-Zagier transform of the HOMFLY-PT polynomial for some infinite families of twisted hyperbolic knots. Among them, we found a family of Pretzel knots for which the transform has a fully factorised form, while for the remaining families considered it consists of sums of factorised terms. Their zeros have a remarkable structure as the modulus of their product always equals unity. |
| title | Harer-Zagier formulas for families of twisted hyperbolic knots |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2307.05919 |