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arXiv:1001.2680 [math.GT]AbstractReferencesReviewsResources

Representations and the colored Jones polynomial of a torus knot

Kazuhiro Hikami, Hitoshi Murakami

Published 2010-01-15Version 1

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.

Comments: 18 pages, 1 figure, submitted to the Proceedings of the workshop "Chern-Simons Gauge Theory: 20 Years After"
Categories: math.GT
Subjects: 57M27, 57M25, 57M50
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