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

TL;DR

This paper explores the relationship between the series knot invariant and ADO-invariants for torus knots, providing explicit formulas, algorithms, and a deformation of the ADO_3-polynomial to deepen understanding of knot invariants.

Contribution

It offers explicit formulas and algorithms for ADO-invariants of torus knots derived from the series invariant, and introduces a deformation of the ADO_3-polynomial.

Findings

Confirmed the relation between series invariant and ADO-invariants for torus knots.

Provided explicit formulas and algorithms for computing these invariants.

Introduced a one-parameter deformation of the ADO_3-polynomial.

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.