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

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

2011-02-17

arxiv.org/abs/1102.3530v1

Mathematics

Geometric Topology

35 pages, 4 figures

Scientific paper

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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