Representations and the colored Jones polynomial of a torus knot

2010/01/15 by Hikami, Kazuhiro, Murakami, Hitoshi
#57M25 #57M27 #57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1001.2680

Abstract

We show that for a torus knot the SL(2;C) Chern-Simons invariants and the SL(2;C) twisted Reidemeister torsions appear in an asymptotic expansion of the colored Jones polynomial. This suggests a generalization of the volume conjecture that relates the asymptotic behavior of the colored Jones polynomial of a knot to the volume of the knot complement.

Related

• The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot
• On the asymptotic expansion of the colored Jones polynomial for torus knots
• On the asymptotic behavior of the colored Jones polynomial of the figure-eight knot associated with a real number
• The colored Jones polynomial of the figure-eight knot and an SL(2;ℝ)-representation
• An introduction to the volume conjecture and its generalizations