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 $$N \in {\mathbb {N}}$$ N ∈ , describe the invariant $$J_N(L,q)$$ J ( L , q ) as graded intersection pairing of certain homology classes in covering configuration space on punctured disc. This construction is based Lawrence representation and result due to Kohno that relates quantum representations braid groups.