Torus knot state asymptotics

Details Torus knot state asymptotics Torus knot state asymptotics

2011-07-23

arxiv.org/abs/1107.4692v1

Mathematics

Geometric Topology

32 pages

Scientific paper

The state of a knot is defined in the realm of Chern-Simons topological quantum field theory as a holomorphic section on the SU(2) character manifold of the peripheral torus. We compute the asymptotics of the torus knot states in terms of the Alexander polynomial, the Reidemeister torsion and the Chern-Simons invariant. We also prove that the microsupport of the torus knot state is included in the character manifold of the knot exterior. As a corollary we deduce the Witten asymptotics conjecture for the Dehn filling of the torus knots and asymptotic expansions for the colored Jones polynomials.

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