纽结与多项式

Knots and Polynomials

中文关键词:  纽结  Jones多项式  Laurent多项式.

英文关键词:knot  Jones polynomial  Laurent polynomial.

中文摘要:

      在本文中,我们通过运用纽结多项式的基本性质(例如:纽结多项式在一些特殊点的值, Arf不变量和纽结多项式的微分性质)来研究一些纽结和多项式之间的关系.给出一个宽度不超过5的整系数Laurent多项式是某个纽结的Jones多项式的充分必要条件.

英文摘要:

      In this paper, we deal with some corresponding relations between knots and polynomials by using the basic properties of knot polynomials (such as, some special values of knot polynomials, the Arf invariant and derivative of knot polynomials). We give necessary and sufficient conditions that a Laurent polynomial with integer coefficients, whose breadth is less than five, is the Jones polynomial of a certain knot.