Single-colored ADO-3 invariant is a specialization of Links-Gould invariant for closures of 5-braids

TL;DR

This paper shows that for knots and links formed from 5-braids, the single-colored ADO-invariant matches the Links-Gould polynomial with certain variables, suggesting a broader equivalence.

Contribution

It establishes a specific equivalence between the ADO-invariant and the Links-Gould polynomial for 5-braid closures and conjectures this extends to all knots and links.

Findings

For 5-braid closures, the invariants coincide.

Conjecture that the equivalence holds universally.

Provides arguments supporting the conjecture.

Abstract

We prove that for knots and links that are closures of 5-braids, single-colored ADO-invariant of third order coincides with Links-Gould polynomial with specific choice of variables. We also conjecture that this is true for any knots and links and provide some arguments for that.