Affine representations of rational and pretzel knots
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909825181417472 |
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| author | Martínez, Javier |
| author_facet | Martínez, Javier |
| contents | We construct and study representations of rational and pretzel tangle and knot groups into the affine group $\mathrm{AGL}(1,\mathbb{C})$, via a TQFT that is valued in the category of spans of singular vector bundles over $\mathbb{C}^{\ast}$. For these families, we derive closed-form expressions for their Alexander polynomials and establish bounds on their zeros. Finally, we specialize the functor at $t=-1$ and analyze colorings of rational tangles in terms of spans of complex vector spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affine representations of rational and pretzel knots Martínez, Javier Geometric Topology Quantum Algebra Representation Theory 57K14, 14M35, 57K12, 18M20 We construct and study representations of rational and pretzel tangle and knot groups into the affine group $\mathrm{AGL}(1,\mathbb{C})$, via a TQFT that is valued in the category of spans of singular vector bundles over $\mathbb{C}^{\ast}$. For these families, we derive closed-form expressions for their Alexander polynomials and establish bounds on their zeros. Finally, we specialize the functor at $t=-1$ and analyze colorings of rational tangles in terms of spans of complex vector spaces. |
| title | Affine representations of rational and pretzel knots |
| topic | Geometric Topology Quantum Algebra Representation Theory 57K14, 14M35, 57K12, 18M20 |
| url | https://arxiv.org/abs/2510.02077 |