纽结的Alexander多项式的微分性质  

Differential Properties of Alexander Polynomials of Knots

作　　者：韩友发[1] 王泓月 燕佳钰 孙思宇 HAN You-fa;WANG Hong-yue;YAN Jia-yu;SUN Si-yu(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：《通化师范学院学报》2022年第4期36-40,共5页Journal of Tonghua Normal University

基　　金：国家自然科学基金项目(11471151);辽宁省教育厅科学技术项目(LJ2019004)。

摘　　要：通过使用拆接关系式的方式和一般的求导法则对纽结的Alexander多项式的各阶微分进行计算,研究变量t取得某一特殊值时,所得计算结果的整除性质.分别计算了Twist纽结、n个Twist纽结的连通和的Alexander多项式在变量t取不同值时其各阶微分的不同特性.给出任意纽结的Alexander多项式的各阶微分的计算公式.By using the disassembly relation and the general derivation rule to calculate the differential of each order of the Alexander polynomial of the knot,the divisibility of the calculation result obtained when the variable obtains a special value is studied. The differential characteristics of Alexander polynomials of twist knots and connected sums of twist knots are calculated respectively when the variables take different values. The calculation formula of differential of every order of Alexander polynomial with arbitrary knot is given.

关 键 词：Alexander多项式 高阶微分 Twist纽结 

分 类 号：O189.3[理学—数学]