摘要
主要讨论具有两个分支环链L的几个多项式不变量的微分性质.对环链L的Jones多项式V(L;t)以及在Jones多项式基础上定义的几个L的多项式不变量X(L;t),Φ(L;t)求k阶导数,并研究它们在t=1时的整除性质,即V(k)(L;1),Φ(k)(L;1)和φ(k)(L;1)的整除性质.先将环链L用拆接关系式分解成纽结的形式,然后根据纽结的多项式不变量性质,得到具有两个分支的环链多项式不变量性质,进而得到L的多项式不变量的性质.
This paper mainly deals with the differential properties of several polynomial invariants of link L with two components.We solve for kth derivatives of several polynomial invariants X（L;t）,Φ（L;t）of L based on the Jones polynomial and the Jones polynomial V（L;t）of link L,meanwhile,investigate the divisibility of them when t=1,that is the divisibility of V^（k）（L;1）,Φ^（k）（L;1）and φ^（k）（L;1）.In the paper,we decompose the link L into knots forms through skein relation.Firstly we get the properties of link polynomials with two components,according to the polynomial invariant of knot.Then,we obtain the properties of polynomial invariant of link L.
出处
《辽宁师范大学学报（自然科学版）》
CAS
2010年第3期277-280,共4页
Journal of Liaoning Normal University:Natural Science Edition
基金
国家自然科学基金项目(10771023)
辽宁省教育厅高等学校科研项目(2009A418)
