The Alexander polynomial of twisted torus knots
Geometric Topology
2025-09-10 v3
Abstract
Twisted torus knots are a generalization of torus knots, obtained by introducing additional full twists to adjacent strands of the torus knots. In this article, we present an explicit formula for the Alexander polynomial of twisted torus knots. Our approach utilizes a presentation of the knot group of twisted torus knots combined with Fox's free differential calculus. As applications, we provide a lower bound for the genus of certain families of twisted torus knots and identify families of twisted torus knots that are not -space knots.
Keywords
Cite
@article{arxiv.2411.13003,
title = {The Alexander polynomial of twisted torus knots},
author = {Adnan and Kyungbae Park},
journal= {arXiv preprint arXiv:2411.13003},
year = {2025}
}
Comments
17 pages, 6 figures; revised according to referee's suggestions; notational typos corrected; to appear in J. Knot Theory Ramifications