一类3-缠绕的Jones多项式
The Jones Polynomials of a Class of 3-Tangles
DOI: 10.12677/AAM.2022.1110778, PDF,   
作者: 杨晓雨：辽宁师范大学，辽宁 大连
关键词: Jones多项式；不变量；3-缠绕；Jones Polynomial； Invariant； 3-Tangle
摘要: 选定了3-缠绕的一种定向方式，结合Giller的房间理论给出任意两个3-缠绕的复合的Jones多项式。接着，通过研究计算得到了一类特殊3-缠绕的Jones多项式的递推公式以及由其闭包所形成的链环的Jones多项式。
Abstract: An unusual orientation of 3-tangles is given, and the Jones polynomial of the concatenation of two 3-tangles is given by Giller’s room theory. Then, the recursion formula of the Jones polynomials of a special kind of 3-tangles is obtained by studying and calculating. In addition, the formula to obtain the Jones polynomial of the links obtained from their closure is given.
文章引用：杨晓雨. 一类3-缠绕的Jones多项式[J]. 应用数学进展, 2022, 11(10): 7325-7333. https://doi.org/10.12677/AAM.2022.1110778

参考文献

[1] Alexander, J.W. (1928) Topological Invariants of Knots and Links. Transactions of the American Mathematical Society, 30, 275-306. [Google Scholar] [CrossRef] 
[2] Conway, J.H. (1970) An Enumeration of Knots and Links and Some of Their Algebraic Properties. Computational Problems in Abstract Algerbra, 22, 329-358. [Google Scholar] [CrossRef] 
[3] Jones, V.F.R. (1985) A Polynomial Invariants for knots via von Neumann Algebras. Bulletin of the American Mathematical Society, 12, 103-111. [Google Scholar] [CrossRef] 
[4] Freyd, P., Yetter, D., Hoste, J., et al. (1985) A New Pol-ynomial Invariant of Knots and Links. Bulletin of the American Mathematical Society, 12, 239-246. [Google Scholar] [CrossRef] 
[5] Cabrera-Ibarra, H. (2003) On the Classification of Rational 3-Tangles. Journal of Knot Theory and Its Ramifications, 12, 921-946. [Google Scholar] [CrossRef] 
[6] Cabrera-Ibarra, H. (2004) Conway Polynomial of the Closures of Oriented 3-String Tangles. Boletín de la Sociedad Matemática Mexicana, 10, 55-62.
[7] Cabrera-Ibarra, H. (2004) Results on the Classification of Rational 3-Tangles. Journal of Knot Theory and Its Ramifications, 13, 175-192. [Google Scholar] [CrossRef] 
[8] Cabrera-Ibarra, H. and Lizárraga, D.A.L. (2010) An Algorithm Based on 3-Braids to Solve Tangle Equations Arising in the Action of Gin DNA Invertase. Applied Mathematics and Computation, 216, 95-106. [Google Scholar] [CrossRef] 
[9] Lizárraga, D.A., Hernández, L.Y. and Cabrera-Ibarra, H. (2012) Computing the Conway Polynomial of Several Closures of Oriented 3-Braids. Topology and Its Applications, 159, 1195-1209. [Google Scholar] [CrossRef] 
[10] de los Angeles Guevara Hernández, M. and Cabre-ra-Ibarra, H. (2019) Infinite Families of Prime Knots with alt(K) = 1 and Their Alexander Polynomials. Journal of Knot Theory and Its Ramifications, 28, Article ID: 1950010. [Google Scholar] [CrossRef] 
[11] Adams, C. (1994) The Knot Book. W. H. Freeman and Com-pany, New York.
[12] Giller, C.A. (1982) A Family of Links and the Conway Calculus. Transactions of the American Mathematical Society, 270, 75-109. [Google Scholar] [CrossRef] 
[13] 姜伯驹. 绳圈的数学[M]. 大连: 大连理工大学出版社, 2011.
[14] Murasugi, K. (2007) Knot Theory and Its Applications. Springer Science & Business Media, Berlin. [Google Scholar] [CrossRef] 

为你推荐