纽结的琼斯多项式与罗朗多项式

摘要

In this paper,we deal with some relations between the Jones polynomial of knot and the Laurent polynomial by using their properties(such as,some special values of the Jones polynomial and derivative of knot polynomials).We give necessary conditions that a Laurent polynomial,with degree eight or nine,is the Jones polynomial of a certain knot.Furthermore,we give the properties of Arf invariant for knot.%本文利用纽结的琼斯多项式和罗朗多项式的性质,研究了二者之间的关系.主要是利用纽结多项式的微分性质以及多项式在某些特殊点的值.给出了次数小于10罗朗多项式是某个纽结的琼斯多项式的必要条件.进而研究了纽结的Arf不变量的性质.