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arxiv: 1001.2680 · v1 · submitted 2010-01-15 · 🧮 math.GT

Representations and the colored Jones polynomial of a torus knot

classification 🧮 math.GT
keywords knotcoloredjonespolynomialasymptotictorusvolumeappear
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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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