On the formulae for the colored HOMFLY polynomials
Geometric Topology
2012-11-19 v2 High Energy Physics - Theory
Abstract
We provide methods to compute the colored HOMFLY polynomials of knots and links with symmetric representations based on the linear skein theory. By using diagrammatic calculations, several formulae for the colored HOMFLY polynomials are obtained. As an application, we calculate some examples for hyperbolic knots and links, and we study a generalization of the volume conjecture by means of numerical calculations. In these examples, we observe that asymptotic behaviors of invariants seem to have relations to the volume conjecure.
Keywords
Cite
@article{arxiv.1210.7574,
title = {On the formulae for the colored HOMFLY polynomials},
author = {Kenichi Kawagoe},
journal= {arXiv preprint arXiv:1210.7574},
year = {2012}
}
Comments
12 pages, 13 figures, explanations in the proofs and figures are added