On the determinant of checkerboard colorable virtual knots
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917418551476224 |
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| author | Hatano, Tomoaki Nozaki, Yuta |
| author_facet | Hatano, Tomoaki Nozaki, Yuta |
| contents | For classical knots, Murasugi showed that the determinant modulo $8$ is classified by the Arf invariant. Boden and Karimi introduced a determinant for checkerboard colorable virtual knots. We prove that this determinant modulo $8$ is classified by the coefficient of $z^2$ in the ascending polynomial, an extension of the Conway polynomial for classical knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the determinant of checkerboard colorable virtual knots Hatano, Tomoaki Nozaki, Yuta Geometric Topology 57K12 (Primary) 57K10, 57K16 (Secondary) For classical knots, Murasugi showed that the determinant modulo $8$ is classified by the Arf invariant. Boden and Karimi introduced a determinant for checkerboard colorable virtual knots. We prove that this determinant modulo $8$ is classified by the coefficient of $z^2$ in the ascending polynomial, an extension of the Conway polynomial for classical knots. |
| title | On the determinant of checkerboard colorable virtual knots |
| topic | Geometric Topology 57K12 (Primary) 57K10, 57K16 (Secondary) |
| url | https://arxiv.org/abs/2408.01891 |