Invariants of links of Conway type
Invariants of links of Conway type
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发表时间：
1988-02
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通讯作者：
J. Przytycki;Pawel Traczyk
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作者：
J. Przytycki;Pawel Traczyk
本文的目的是提出一种构造定向链同位素类不变量的组合方法。这是对Conway和Jones的多项式不变量的推广。这些不变量有一个显著的共同特征。如果L+， L-和L0是相同的定向链接图，除了在一个交叉点附近（如Conway或Jones多项式），那么不变量w(L)具有以下性质：w（L+）唯一由w（L-）和w（L0）决定，并且w（L-）唯一由w（L+）和w（L0）决定。为了形式化这个性质，我们引入了康威代数和拟康威代数的概念。这篇论文现在已经有32年的历史了，它包含了对HOMFLYPT多项式的PT贡献。我们相信它应该在arXiv中可用。
The purpose of this paper is to present a certain combinatorial method of constructing invariants of isotopy classes of oriented tame links. This arises as a generalization of the known polynomial invariants of Conway and Jones. These invariants have one striking common feature. If L+, L- and L0 are diagrams of oriented links which are identical, except near one crossing point (as in Conway or Jones polynomials), then an invariant w(L) has the property: w(L+) is uniquely determined by w(L-) and w(L0), and also w(L-) is uniquely determined by w(L+) and w(L0). To formalize this property we introduce a concept of a Conway algebra and quasi Conway algebra. The paper is now almost 32 years old and it contains the PT contribution to HOMFLYPT polynomial. We believe it should be available in arXiv.