N价图的P2(G)不变量
P2(G) Invariant of N-Valent Graphs
DOI: 10.12677/aam.2025.148375, PDF,    国家自然科学基金支持
作者: 杨 琦*, 李 佳, 冷旭东:辽宁师范大学数学学院,辽宁 大连
关键词: 空间图嵌入图不变量着色Jones多项式Spatial Graph N-Valent Embedded Graphs Colored Jones Polynomial
摘要: 本文主要利用Jones-Wenzl幂等元的递归关系式中当n = 2时的情况,给出了n价顶点拆接关系式,根据该拆接关系式给出n价空间图的P2(G)不变量。
Abstract: This paper mainly uses the case when n=2 in the recursive relation of Jones-Wenzl idempotents to present the skein relation of n-valent vertices, and based on this skein relation, gives the invariant of n-valent spatial graphs.
文章引用:杨琦, 李佳, 冷旭东. N价图的P2(G)不变量[J]. 应用数学进展, 2025, 14(8): 109-116. https://doi.org/10.12677/aam.2025.148375

参考文献

[1] Kauffman, L.H. (1987) State Models and the Jones Polynomial. Topology, 26, 395-407. [Google Scholar] [CrossRef
[2] Jones, V.F.R. (1985) A Polynomial Invariant for Knots via Von Neumann Algebras. Bulletin of the American Mathematical Society, 12, 103-111. [Google Scholar] [CrossRef
[3] Witten, E. (1989) Quantum Field Theory and the Jones Polynomial. Communications in Mathematical Physics, 121, 351-399. [Google Scholar] [CrossRef
[4] Reshetikhin, N. and Turaev, V.G. (1991) Invariants of 3-Manifolds via Link Polynomials and Quantum Groups. Inventiones Mathematicae, 103, 547-597. [Google Scholar] [CrossRef
[5] Kauffman, L.H. and Lins, S. (1994) Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds. Princeton University Press.
[6] Prasolov, V.V. and Sossinsky, A.B. (1996) Knots, Links, Braids and 3-Manifolds: An Introduction to the New Invariants in Low-Dimensional Topology (Translations of Mathematical Monographs, Vol. 154). American Mathematical Society, 171-176. [Google Scholar] [CrossRef
[7] Yamada, S. (1989) An Invariant of Spatial Graphs. Journal of Graph Theory, 13, 537-551. [Google Scholar] [CrossRef