图8.8.4格的链环分支数

链环分支数与符号平图之间有一一对应关系,这种对应是通过中间图来实现的,它提供了通过图研究链环的一个方法.在二十世纪八十年代末,这一对应就被用于建立纽结理论中的琼斯多项式的关系,但链环分支数与对应平图的符号无关,链环分支数是链环的最简单的一个不变量,求符号平图对应链环分支数是通过平图研究链环的最基本的问题之一,本文确定了8.8.4格的链环分支数.

Determining the Component Number of Links Corresponding to 8.8.4 Lattices

There is a one-to-one correspondence between signed plane graphs and link diagrams via the medial construction. Indeed, it provides a method of studying links using graphs. In the late 1980s, the correspondence was used to obtain a relation between Jones polynomial in kont theory and Tutte polynomial in graph theory. The component number of the corresponding link diagrams is however independent of the signs of the plane graph. One of the first problems in studying links by using graphs via this correspondence may be that of determining the component number of the link diagrams corresponding to a signed plane graph. In this paper, we shall determine the component numbers of links corresponding to 8.8.4 lattices.