Topological formula of the loop expansion of the colored Jones polynomials

2014/11/20 by Tetsuya Ito, Ito, Tetsuya
Mathematics · #57M27 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1411.5418

openalex publication_date 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a topological formula of the loop expansion of the colored Jones polynomials by using identification of generic quantum sl2 representation with homological representations. This gives a direct topological proof of the Melvin-Morton-Rozansky conjecture, and a connection between entropy of braids and quantum representations.

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