Geodesic
The zero stability for the one-row colored 𝔰𝔩3-Jones polynomial
Yuasa, Wataru1
1Graduate 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
Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 1917-1944
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The stability of coefficients of colored (𝔰𝔩2-) Jones polynomials {JK,n𝔰𝔩2(q)}n was discovered by Dasbach and Lin. This stability is now called the zero stability of JK,n𝔰𝔩2(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 𝔰𝔩3-Jones polynomials {JK,n𝔰𝔩3(q)}n for B-adequate links L with antiparallel twist regions by using the linear skein theory based on Kuperberg’s 𝔰𝔩3-webs. This implies the existence of many q-series obtained from a quantum invariant associated with 𝔰𝔩3.

DOI : 10.2140/agt.2025.25.1917
Keywords: colored Jones polynomial, tails of knots, $q$-series

Yuasa, Wataru  1

1 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 
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Yuasa, Wataru. The zero stability for the one-row colored 𝔰𝔩3-Jones polynomial. Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 1917-1944. doi: 10.2140/agt.2025.25.1917

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