Topological formula of the loop expansion of the colored Jones polynomials

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.

arXiv comment14 pages, 4 figures

References in corpus (3)

• Braid Groups are Linear
• The hyperbolic volume of knots from quantum dilogarithm
• The lines of the Kontsevich integral and Rozansky's rationality conjecture

Cited by in corpus (1)

• A non-commutative Reidemeister-Turaev torsion of homology cylinders