Periodicity Properties of the Colored Jones Polynomial
Geometric Topology
2016-06-02 v1
Abstract
The "color" in the colored Jones polynomial is an integer parameter. In this paper, a periodic pattern of the values of the colored Jones polynomial at the second and the third roots of unity is found. If we substitute -1 to the colored Jones polynomial, the value is alternately 1 or the determinant of the given link. When it comes to substituting the primitive third root of unity, another periodic pattern appears.
Cite
@article{arxiv.1606.00125,
title = {Periodicity Properties of the Colored Jones Polynomial},
author = {Hiroki Murakami},
journal= {arXiv preprint arXiv:1606.00125},
year = {2016}
}
Comments
4 pages