The zero stability for the one-row colored 𝔰𝔩3-Jones polynomial

Yuasa, Wataru

doi:10.2140/agt.2025.25.1917

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The zero stability for the one-row colored $\mathfrak{sl}_3$-Jones polynomial

Wataru Yuasa

Algebraic & Geometric Topology 25 (2025) 1917–1944

DOI: 10.2140/agt.2025.25.1917

Abstract

The stability of coefficients of colored ( ${𝔰 𝔩}_{2}$ -) Jones polynomials ${J_{K, n}^{{𝔰 𝔩}_{2}} (q)}_{n}$ was discovered by Dasbach and Lin. This stability is now called the zero stability of $J_{K, n}^{{𝔰 𝔩}_{2}} (q)$ . Armond showed zero stability for a $B$ -adequate link by using the linear skein theory based on the Kauffman bracket. We prove the zero stability of one-row colored ${𝔰 𝔩}_{3}$ -Jones polynomials ${J_{K, n}^{{𝔰 𝔩}_{3}} (q)}_{n}$ for $B$ -adequate links $L$ with antiparallel twist regions by using the linear skein theory based on Kuperberg’s ${𝔰 𝔩}_{3}$ -webs. This implies the existence of many $q$ -series obtained from a quantum invariant associated with ${𝔰 𝔩}_{3}$ .

Keywords

colored Jones polynomial, tails of knots, $q$-series

Mathematical Subject Classification

Primary: 57K10, 57K14, 57K16

References

Publication

Received: 27 August 2020

Revised: 7 October 2023

Accepted: 10 March 2024

Published: 11 August 2025

Authors

Wataru Yuasa
Graduate School of Science Division of Mathematics and Mathematical Sciences Kyoto University Kyoto Japan	International Institute for Sustainability with Knotted Chiral Meta Matter Hiroshima University Hiroshima Japan
https://wataruyuasa.github.io/math/

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Volume 25, issue 4 (2025)