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arXiv · 2307.05919

Harer-Zagier formulas for families of twisted hyperbolic knots

Andreani Petrou·Shinobu Hikami
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Abstract

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.

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Andreani Petrou, Shinobu Hikami. 2023-07-12. Harer-Zagier formulas for families of twisted hyperbolic knots. https://doi.org/10.1088/1751-8121/ad421b

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