A topological model for the coloured Jones polynomials

2017/12/13 by Cristina Ana-Maria Anghel, Anghel, Cristina Ana-Maria
Mathematics · #16T05 #16T25 #20F36 #57M25 #57M27 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1712.04873

openalex publication_date 2017/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we will present a homological model for Coloured Jones Polynomials. For each colour N ∈ \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.

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