一类链环的HOMFLY多项式

The HOMFLY Polynomials of Class of Links

摘要: 纽结理论中主要研究对象为纽结和链环，对它们的研究是通过所对应的纽结投影图来展开的。纽结多项式是一类以多项式表达的纽结不变量，例如Alexander多项式和Jones多项式。HOMFLY多项式是一个双变量的Laurent多项式，两个变量分别是m和l，是继Jones多项式之后，又一计算纽结不变量的多项式。Brunnian链环是一类特殊的链环，拆去任何单个分量都会生成一个平凡链环。本文主要结合HOMFLY多项式的定义和性质，应用拆接关系研究计算Brunnian链环的HOMFLY多项式。

Abstract: The main research objects in knot theory are knots and links, but the research on them is carried out through the corresponding knot projection diagram. The knot polynomial refers to a class of knot invariant expressed by polynomials, such as the Alexander polynomial and the Jones polynomial. The HOMFLY polynomial is a bivariate Laurent polynomial with two variables m and l, which is another important polynomial for calculating knots after the Jones polynomial. Brunnian link is a special class of link in which the complement of any one component is a trivial link. In this paper, we state and calculate the HOMFLY polynomials of Brunnian link by using the definition and properties of HOMFLY polynomials and the disconnection relation.