两类Pretzel链环的着色Jones多项式
The Colored Jones Polynomial of Two Types of Pretzel Links
DOI: 10.12677/pm.2026.164092, PDF,   
作者: 刘 娜：浙江师范大学数学科学学院，浙江 金华
关键词: 纽结；Skein理论；着色Jones多项式；Knot； Skein Theory； The Colored Jones Polynomial
摘要: (−2,3,2p+3)-pretzel纽结和(−2,3,2p)-pretzel链环为低维拓扑的理论研究提供了两类重要例子。例如，(−2,3,7)-pretzel纽结与52结具有相同的双曲体积，(−2,3,8)-pretzel链环和Whitehead链环具有相同的双曲体积等。本文主要利用Kauffman bracket skein理论计算了(−2,3,2p+3)-pretzel纽结和(−2,3,2p)-pretzel链环的着色Jones多项式的显示公式，这些公式对于量子拓扑中AJ猜想、体积猜想等课题的研究发挥作用。
Abstract: The (-2,3,2p+3)-pretzel knots and the (-2,3,2p)-pretzel links provide two important classes of examples for theoretical studies in low-dimensional topology. For instance, the (-2,3,7)-pretzel knot shares the same hyperbolic volume as the 5_2 knot, and the (-2,3,8)-pretzel link shares the same hyperbolic volume as the Whitehead link. In this paper, we employ the Kauffman bracket skein theory to derive explicit formulas for the colored Jones polynomials of the (-2,3,2p+3)-pretzel knots and the (-2,3,2p)-pretzel links. These formulas are expected to contribute to research on topics in quantum topology, such as the AJ Conjecture and the Volume Conjecture.
文章引用：刘娜. 两类Pretzel链环的着色Jones多项式[J]. 理论数学, 2026, 16(4): 65-75. https://doi.org/10.12677/pm.2026.164092

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