Knot Theory With The Lorentz Group

Abstract

We analyse the perturbative expansion of the knot invariants defined from the unitary representations of the Quantum Lorentz Group in two different ways, namely using the Kontsevich Integral and weight systems, and the $R$-matrix in the Quantum Lorentz Group defined by Buffenoir and Roche. The two formulations are proved to be equivalent; and they both yield $C[[h]]$-valued knot invariants related with the Melvin Morton expansion of the Coloured Jones Polynomial.