Harer-Zagier formulas for families of twisted hyperbolic knots
Mathematical Physics
2025-06-11 v2 math.MP
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.
Keywords
Cite
@article{arxiv.2307.05919,
title = {Harer-Zagier formulas for families of twisted hyperbolic knots},
author = {Andreani Petrou and Shinobu Hikami},
journal= {arXiv preprint arXiv:2307.05919},
year = {2025}
}
Comments
9 pages, 9 figures