A Contribution of the Trivial Connection to the Jones Polynomial and Witten's Invariant of 3d Manifolds II

Abstract

We extend the results of our previous paper from knots to links by using a formula for the Jones polynomial of a link derived recently by N. Reshetikhin. We illustrate this formula by an example of a torus link. A relation between the parameters of Reshetikhin's formula and the multivariable Alexander polynomial is established. We check that our expression for the Alexander polynomial satisfies some of its basic properties. Finally we derive a link surgery formula for the loop corrections to the trivial connection contribution to Witten's invariant of rational homology spheres.

26 pages

References in corpus (3)

• A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariant of 3d Manifolds I
• A Large k Asymptotics of Witten's Invariant of Seifert Manifolds
• Reshetikhin's Formula for the Jones Polynomial of a Link: Feynman diagrams and Milnor's Linking Numbers

Cited by in corpus (10)

• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Large N duality beyond the genus expansion
• Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers
• On the Quantum Invariant for the Brieskorn Homology Spheres
• Reshetikhin's Formula for the Jones Polynomial of a Link: Feynman diagrams and Milnor's Linking Numbers
• Quantum Invariants, Modular Forms, and Lattice Points II
• Cabled Wilson Loops in BF Theories
• Knot Invariants and New Weight Systems from General 3D TFTs
• Supersymmetry, homology with twisted coefficients and n-dimensional knots