Knot Complement, ADO-Invariants and their Deformations for Torus Knots

Abstract

A relation between the two-variable series knot invariant and the Akutus-Deguchi-Ohtsuki(ADO)invariant was conjectured recently. We reinforce the conjecture by presenting explicit formulas and/or an algorithm for certain ADO-invariants of torus knots obtained from the series invariant of complement of a knot. Furthermore, one parameter deformation of ADO 3 -polynomial of torus knots is provided. CONTENTS 4 Appendix 132 Background Two-Variable Series Knot ComplementA series invariant F K for a complement of a knot M 3 K was introduced [1]. It has various properties such as the gluing formula and the (Dehn) surgery formula. This knot invariant F K