Polynomials of genus one prime knots of complexity at most five
Geometric Topology
2019-08-27 v1
Abstract
Prime knots of genus one admitting diagram with at most five classical crossings were classified by Akimova and Matveev in 2014. In 2018 Kaur, Prabhakar and Vesnin introduced families of L-polynomials and F-polynomials for virtual knots which are generalizations of affine index polynomial. Here we introduce a notion of totally flat-trivial knots and demonstrate that for such knots F-polynomials and L-polynomials coincide with affine index polynomial. We prove that all Akimova - Matveev knots are totally flat-trivial and calculate their affine index polynomials.
Keywords
Cite
@article{arxiv.1908.09663,
title = {Polynomials of genus one prime knots of complexity at most five},
author = {Maxim Ivanov and Andrei Vesnin},
journal= {arXiv preprint arXiv:1908.09663},
year = {2019}
}
Comments
11 pages, 7 figures, 4 tables