二邻近链环多项式的一个系数  

A coefficient of 2-adjacent link polynomial

作　　者：陶志雄[1] 殷炜栋[1] TAO Zhixiong;YIN Weidong(School of Science,Zhejiang University of Science and Technology,Hangzhou 310023,Zhejiang,China)

机构地区：[1]浙江科技学院理学院,杭州310023

出　　处：《浙江科技学院学报》2023年第3期209-212,共4页Journal of Zhejiang University of Science and Technology

基　　金：浙江省省级国际化线上线下混合式一流课程(浙教办函〔2021〕195号)。

摘　　要：【目的】二分支链环L=L_(1)∪L_(2)称为二邻近于W=W_(1)∪W_(2),假如存在L的两个交叉c1,c2,则改变其中任何1个或同时改变它们2个都得到W。D=D(oc1,oc2)是分别打开这两个交叉所得的链环。为了对链环进行二邻近分类,探讨了二邻近链环多项式的一个系数。【方法】利用文献[1]768-770中关于二邻近链环的结论,对实现链环的二邻近过程进行了仔细的分析,并讨论了各分支之间的链环数的相互关系,借此特别研究了D的Conway多项式z3的系数a3[1]768的表达式。【结果】若两个交叉c1,c2在不同的分支上,则a3(D)=λ2lk(L),λ∈Z。【结论】不可能通过改变两个异号的交叉使得定向的L4a1二邻近于定向的L9n10。[Objective] A two-branch link L=L_(1)∪L_(2) is said to be 2-adjacent to W=W_(1)∪W_(2). If there are two crossings c1, c2 of L, applying crossing change to either of them or both of them yields W, in which D=D(oc1,oc2) denotes the link obtained by smoothing the two crossings. To investigate the 2-adjacent classification of the link, a coefficient of 2-adjacent link polynomial was researched. [Method] the conclusions in the reference [1]768-770 on the 2-adjacent link were made use of, elaborating on the 2-adjacent process to actualize the link and the relationship of the linking number among the branches, and attaching special attention to the expression of the coefficient a3[1] 768 of D's Conway polynomial z3. [Result] If two crossings c1, c2 are on different branches, then a3(D)=λ2lk(L), λ∈Z. [Conclusion] The oriented link L4a1 is unlikely to be 2-adjacent to the oriented link L9n10 by changing two crossings with different signs on different branches.

关 键 词：链环 二邻近 链环不变量 

分 类 号：O189.24[理学—数学]