On the colored Jones polynomials of certain cable of the torus knots

2008/07/30 by Liu, Qihou
#57M27 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0807.4780

Abstract

In this paper, we study the asymptotic behavior of the colored Jones polynomials evaluated at roots of unity for a special class of knots. We show that certain limit is zero as predicted by the volume conjecture.

Related

• A cabling formula for the colored Jones polynomial
• On the head and the tail of the colored Jones polynomial
• An introduction to the volume conjecture and its generalizations
• Representations and the colored Jones polynomial of a torus knot
• The colored Jones polynomial of a cable of the figure-eight knot