Labels instead of coefficients: a label bracket which dominates the Jones polynomial, the Kuperberg bracket, and the normalised arrow polynomial

TL;DR

This paper introduces a new pictorial formalism that produces an invariant surpassing several established knot invariants, including the Jones polynomial, Kuperberg bracket, and normalized arrow polynomial, for classical and virtual knots.

Contribution

The paper develops a novel picture formalism that yields a unifying invariant dominating multiple known knot invariants.

Findings

The new invariant generalizes existing invariants.

It provides a more comprehensive characterization of knots.

The formalism applies to both classical and virtual knots.

Abstract

In the present paper, we develop a picture formalism which gives rise to an invariant that dominates several known invariants of classical and virtual knots: the Jones polynomial, the Kuperberg bracket, and the normalised arrow polynomial.