Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 134, 16 pages      arXiv:2007.13277      https://doi.org/10.3842/SIGMA.2020.134

Knot Complement, ADO Invariants and their Deformations for Torus Knots

John Chae
Univeristy of California Davis, Davis, USA

Received August 20, 2020, in final form December 09, 2020; Published online December 15, 2020

Abstract
A relation between the two-variable series knot invariant and the Akutsu-Deguchi-Ohtsuki (ADO) invariant was conjectured recently. We reinforce the conjecture by presenting explicit formulas and/or an algorithm for particular ADO invariants of torus knots obtained from the series invariant of complement of a knot. Furthermore, one parameter deformation of ${\rm ADO}_3$ polynomial of torus knots is provided.

Key words: torus knots; knot complement; quantum invariant; $q$-series; ADO Polynomials; Chern-Simons theory; categorification.

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