A diagrammatic computation of abelian link invariants
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915636817428480 |
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| author | Cimasoni, David Ferretti, Livio Liu, Jessica |
| author_facet | Cimasoni, David Ferretti, Livio Liu, Jessica |
| contents | We show how the multivariable signature and Alexander polynomial of a colored link can be computed from a single symmetric matrix naturally defined from a colored link diagram. In the case of a single variable, it coincides with the matrix introduced by Kashaev in [arXiv:1801.04632], which was recently proven to compute the Levine-Tristram signature and the Alexander polynomial of oriented links [arXiv:2311.01923, arXiv:2310.16729]. As a corollary, we obtain a multivariable extension of Kauffman's determinantal model of the Alexander polynomial, recovering a result of Zibrowius [arXiv:1601.04915v1]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A diagrammatic computation of abelian link invariants Cimasoni, David Ferretti, Livio Liu, Jessica Geometric Topology 57K10 We show how the multivariable signature and Alexander polynomial of a colored link can be computed from a single symmetric matrix naturally defined from a colored link diagram. In the case of a single variable, it coincides with the matrix introduced by Kashaev in [arXiv:1801.04632], which was recently proven to compute the Levine-Tristram signature and the Alexander polynomial of oriented links [arXiv:2311.01923, arXiv:2310.16729]. As a corollary, we obtain a multivariable extension of Kauffman's determinantal model of the Alexander polynomial, recovering a result of Zibrowius [arXiv:1601.04915v1]. |
| title | A diagrammatic computation of abelian link invariants |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2405.17011 |