A contribution of a U(1)-reducible connection to quantum invariants of links I: R-matrix and Burau representation

Abstract

We use the relation between the quantum su(2) R-matrix and the Burau representation of the braid group in order to study the structure of the colored Jones polynomial of links. We show that similarly to the case of a knot, the colored Jones polynomial of a link can be presented as a formal series in powers of q-1. The coefficients of this series are rational functions of q^(color) whose denominators are powers of the Alexander-Conway polynomial.

arXiv commentLaTeX2e, 78 pages; the text has been substantially changed in order to improve the exposition

References in corpus (1)

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

Cited by in corpus (5)

• Large color $R$-matrix for knot complements and strange identities
• Quantum Hyperbolic State Sum Invariants of 3-Manifolds
• A universal U(1)-RCC invariant of links and rationality conjecture
• On p-adic propreties of the Witten-Reshetikhin-Turaev invariant
• A contribution of a U(1)-reducible connection to quantum invariants of links II: Links in rational homology spheres