Representations and the colored Jones polynomial of a torus knot

Details Representations and the colored Jones polynomial of a torus knot Representations and the colored Jones polynomial of a torus knot

2010-01-15

arxiv.org/abs/1001.2680v1

Mathematics

Geometric Topology

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

Scientific paper

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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