Asymptotic behaviors of the colored Jones polynomials of a torus knot

Mathematics – Geometric Topology

Scientific paper

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7 pages

Scientific paper

We study the asymptotic behaviors of the colored Jones polynomials of torus
knots. Contrary to the works by R. Kashaev, O. Tirkkonen, Y. Yokota, and the
author, they do not seem to give the volumes or the Chern-Simons invariants of
the three-manifolds obtained by Dehn surgeries. On the other hand it is proved
that in some cases the limits give the inverse of the Alexander polynomial.

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