Representations and the colored Jones polynomial of a torus knot

Kazuhiro Hikami; Hitoshi Murakami

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arXiv · 1001.2680

Representations and the colored Jones polynomial of a torus knot

Kazuhiro Hikami·Hitoshi Murakami

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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.

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Kazuhiro Hikami, Hitoshi Murakami. 2010-01-15. Representations and the colored Jones polynomial of a torus knot. https://arxiv.org/abs/1001.2680

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