一类3线缠绕的染色数  

Coloring number of a class of 3-tangles

作　　者：王树新[1] 王一 葛悦 杜怡 WANG Shuxin;WANG Yi;GE Yue;DU Yi(School of Mathematics, Liaoning Normal University, Dalian 116029, China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2021年第4期454-460,共7页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学研究青年项目(LQ2019018);辽宁师范大学教改项目(LS202002)。

摘　　要：纽结和链环的合痕分类是三维流形理论研究的一个核心问题,纽结和链环的各种合痕不变量是研究纽结和链环分类的重要工具.对纽结和链环进行缠绕分解分析是从三维流形组合拓扑的角度出发,研究纽结和链环性质与分类的重要方法,缠绕的染色数是研究缠绕分类的重要合痕不变量.基于以上事实,从缠绕染色出发,在整数缠绕染色的基础上,将2线缠绕的染色问题推广到3线缠绕的染色相关问题,利用缠绕染色的规则,找到了一类3线缠绕的特定染色方法,在这类特定的染色方法下,给出了相应3线缠绕的染色数.The isotopic classification of knots and links is a core problem in the study of three dimensional manifold theory.Isotopic invariants of knots and links are important tool to study the classification of knots and links.From the perspective of the combinatorial topology of 3-dimensional manifolds,tangle decomposition analysis of knots and links is a signification method for studying the properties and classifications of knots and links.The coloring number of tangles is an important isotopic invariant for tangle classification.Based on the above facts,starting from the coloring of tangles,base on the coloring of integer tangles,the coloring problems of 2-tangles is extended to the coloring of 3-tangles,using the coloring rules of tangles,the coloring a class of 3-tangles is discussed.On this basis,a specific coloring method for the corresponding 3-tangles is analyzed and the coloring integer of the tangles are given.

关 键 词：缠绕 染色数 扭转 

分 类 号：O189.3[理学—数学]