The colored Jones polynomial, the ChernSimons invariant, and the Reidemeister torsion of a twiceiterated torus knot
Abstract
A generalization of the volume conjecture relates the asymptotic behavior of the colored Jones polynomial of a knot to the ChernSimons invariant and the Reidemeister torsion of the knot complement associated with a representation of the fundamental group to the special linear group of degree two over complex numbers. If the knot is hyperbolic, the representation can be regarded as a deformation of the holonomy representation that determines the complete hyperbolic structure. In this article we study a similar phenomenon when the knot is a twiceiterated torus knot. In this case, the asymptotic expansion of the colored Jones polynomial splits into sums and each summand is related to the ChernSimons invariant and the Reidemeister torsion associated with a representation.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.2714
 Bibcode:
 2014arXiv1402.2714M
 Keywords:

 Mathematics  Geometric Topology
 EPrint:
 54 pages. Submitted to the proceedings of the conference "The Quantum Topology and Hyperbolic Geometry" in Nha Trang, Vietnam, 1317 May, 2013