The colored Jones polynomial of a cable of the figure-eight knot

2020/10/08 by Murakami, Hitoshi, Tran, Anh T.
#FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2010.03698

Abstract

We study the asymptotic behavior of the N-dimensional colored Jones polynomial of a cable of the figure-eight knot, evaluated at exp(ξ/N) for a real number ξ. We show that if ξ is sufficiently large, the colored Jones polynomial grows exponentially when N goes to the infinity. Moreover the growth rate is related to the Chern-Simons invariant of the knot exterior associated with an SL(2;ℝ) representation.

Related

• The asymptotic behaviors of the colored Jones polynomials of the figure eight-knot, and an affine representation
• 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
• Colored Jones polynomials with polynomial growth
• On the colored Jones polynomials of certain cable of the torus knots