Quantum enhancement polynomials associated with the canonical two-element tricbracket

Yuya Koda; Yuya Nishimura; Yuka Sakamoto

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arXiv · 2501.15112

Quantum enhancement polynomials associated with the canonical two-element tricbracket

Yuya Koda·Yuya Nishimura·Yuka Sakamoto

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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.

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Yuya Koda, Yuya Nishimura, Yuka Sakamoto. 2025-01-25. Quantum enhancement polynomials associated with the canonical two-element tricbracket. https://arxiv.org/abs/2501.15112

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