2026/02/28 by Ben Webster, Meri Zaimi
Mathematics · #math.GT #math.QA #math.RT
We prove a conjecture relating augmentation varieties to the large N limit of Chern-Simons theory. Although this does not directly establish that the augmentation polynomial of a knot is the classical limit of a deformed A-polynomial - as suggested by Aganagić and Vafa - it reduces the problem to characterizing certain algebraic properties of a module over the quantum torus, introduced in work of Gaiotto, Kannagi, and Sanjurjo. We term this the HOMFLYPT difference module, which captures relations between the colored HOMFLYPT polynomials of different antisymmetric colorings. We demonstrate that the classical limit of this difference module for a knot is precisely the degree 0 abelianized knot contact homology of the knot, and we provide a natural extension of this result to links.