Knot Complement, ADO Invariants and their Deformations for Torus Knots

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 the complement of a knot. Furthermore, one parameter deformation of the ADO₃ polynomial of torus knots is provided.