Quantum enhancement polynomials associated with the canonical two-element tricbracket

TL;DR

This paper introduces universal quantum enhancement polynomials for the canonical two-element tribracket, demonstrating they are stronger than the Jones polynomial and providing computational results for links with up to 10 crossings.

Contribution

It establishes that quantum enhancement polynomials for this tribracket can be derived from five universal polynomials, advancing link invariant theory.

Findings

Universal polynomials recover quantum enhancement polynomials

Polynomials are strictly stronger than Jones polynomial

Computational results for links up to 10 crossings

Abstract

Quantum enhancement polynomials are invariants for oriented links, defined in association with an algebraic structure called a tribracket. In this paper, we focus on the particular case of the canonical two-element tribracket. We prove that, in that case, the quantum enhancement polynomials can be recovered by five specific polynomials, which we refer to as the universal quantum enhancement polynomials. After presenting several notable properties of these polynomials, we show that they are strictly stronger than the Jones polynomial. Furthermore, we provide computational results for links with up to 10 crossings.