Affine representations of rational and pretzel knots

Javier Martínez

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arXiv · 2510.02077

Affine representations of rational and pretzel knots

Javier Martínez

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Abstract

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.

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Javier Martínez. 2025-10-02. Affine representations of rational and pretzel knots. https://arxiv.org/abs/2510.02077

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