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

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

1998-06-01

arxiv.org/abs/math/9806004v3

Mathematics

Quantum Algebra

LaTeX2e, 78 pages; the text has been substantially changed in order to improve the exposition

Scientific paper

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.

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