纽结多项式的性质

The Properties of Knot Polynomials

主要是研究具有n个分支环链的Jones多项式的性质.首先,讨论了与可定向整同调三维球不变量τ(M)=1+∑∞k=1λk(t-1)k相关的几个环链多项式X(L;t),Φ(L;t)的性质;其次,研究了它们在t=1时的整除性质,即V(k)(L;1),Φk(L)和Φk(L)的整除性质.最后给出了这些性质的一个应用.

In this paper, we deal with the differential properties of Jones polynomial invariants of links with two components. First, we discuss the properties of some polynomials （such as X（ L;t ）, Φ（（L;t））of links which are closed relation with the invariant τ（M）=1＋∑k=1^∞λk（t-1）^k of the integral homology 3-sheres. Second, the divisibility of V^（k）（L; 1）,Φ（k（L）, Φ（k（L） is studied when t = 1. Finally,we give applications of these properties.