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.