纽结理论在数论中的应用  

An application of knot theory in number theory.

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

机构地区：[1]浙江科技学院理学院,浙江杭州310023

出　　处：《浙江大学学报（理学版）》2020年第3期312-314,共3页Journal of Zhejiang University（Science Edition）

摘　　要：基于纽结理论,利用Torus纽结T(m,n)(m,n须为互素)及Jones多项式和Alexander多项式在二阶导数下的性质,证明了(m^2-1)(n^2-1),(m-1)(n-1)(2mn-m-n-1)可分别被24与12整除。Based on the knot theory,this paper shows that(m^2-1)(n^2-1),(m-1)(n-1)(2mn-m-n-1)are divisible by 24 and 12,respectively,by using the properties of the second derivatives of the Jones polynomial and Alexander polynomial of T(m,n)and that m,n must be coprime for Torus knot T(m,n).

关 键 词：数论 Alexander多项式 JONES多项式 Torus纽结 

分 类 号：O189.24[理学—数学]