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...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。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.展开更多
Starting from the free field realization of Kac-Moody Lie algebra,we define a generalized Yang-Yang function.Then for the Lie algebra of type An,we derive braiding and fusion matrix by braiding the thimble from the ge...Starting from the free field realization of Kac-Moody Lie algebra,we define a generalized Yang-Yang function.Then for the Lie algebra of type An,we derive braiding and fusion matrix by braiding the thimble from the generalized Yang-Yang function.One can construct a knots invariant H(K)from the braiding and fusion matrix.It is an isotropy invariant and obeys a skein relation.From them,we show that the corresponding knots invariant is HOMFLY polynomial.展开更多
文摘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。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.
文摘Starting from the free field realization of Kac-Moody Lie algebra,we define a generalized Yang-Yang function.Then for the Lie algebra of type An,we derive braiding and fusion matrix by braiding the thimble from the generalized Yang-Yang function.One can construct a knots invariant H(K)from the braiding and fusion matrix.It is an isotropy invariant and obeys a skein relation.From them,we show that the corresponding knots invariant is HOMFLY polynomial.
