Representations and the colored Jones polynomial of a torus knot

Kazuhiro Hikami; Hitoshi Murakami

Representations and the colored Jones polynomial of a torus knot

Geometric Topology 2010-01-18 v1

Authors: Kazuhiro Hikami , Hitoshi Murakami

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.

Keywords

colored Jones polynomial torus knot Chern-Simons invariants Reidemeister torsion volume conjecture asymptotic expansion

Cite

@article{arxiv.1001.2680,
  title  = {Representations and the colored Jones polynomial of a torus knot},
  author = {Kazuhiro Hikami and Hitoshi Murakami},
  journal= {arXiv preprint arXiv:1001.2680},
  year   = {2010}
}

Comments

18 pages, 1 figure, submitted to the Proceedings of the workshop "Chern-Simons Gauge Theory: 20 Years After"

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