The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of the figure-eight knot

Hitoshi Murakami

doi:10.1112/jtopol/jts036

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arXiv · 1102.3530

The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of the figure-eight knot

Hitoshi Murakami

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Abstract

We show that from the asymptotic behavior of an evaluation of the colored Jones polynomial of the figure-eight knot we can extract the Chern--Simons invariant and the twisted Reidemeister torsion associated with a representation of the fundamental group of the knot complement to the two-dimensional complex special linear group.

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Hitoshi Murakami. 2011-02-17. The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of the figure-eight knot. https://doi.org/10.1112/jtopol%2Fjts036

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