A topological model for the coloured Jones polynomials

Abstract

In this paper we will present a homological model for Coloured Jones Polynomials. For each colour N in {mathbb {N}}, we will describe the invariant J_N(L,q) as a graded intersection pairing of certain homology classes in a covering of a configuration space on the punctured disc. This construction is based on the Lawrence representation and a result due to Kohno that relates quantum representations and homological representations of the braid groups.