On the formulae for the colored HOMFLY polynomials

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.

12 pages, 13 figures, explanations in the proofs and figures are added

References in corpus (2)

• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots
• An introduction to the volume conjecture and its generalizations

Cited by in corpus (1)

• The colored HOMFLY polynomial is q-holonomic