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A topological model for the coloured Jones polynomials (1712.04873v2)
Published 13 Dec 2017 in math.GT, math.QA, and math.RT
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 the configuration space on the punctured disk. 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.