Torus knot state asymptotics

2011/07/23 by Laurent Charles, Charles, Laurent
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1107.4692

openalex publication_date 2011/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups
• Knot state asymptotics I, AJ Conjecture and abelian representations

Related

• Knot state asymptotics II, Witten conjecture and irreducible representations
• Knot state asymptotics I, AJ Conjecture and abelian representations
• Representations and the colored Jones polynomial of a torus knot
• On the asymptotic expansion of the colored Jones polynomial for torus knots
• The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot