纽结补中不可压缩且配对不可压缩曲面的性质

Properties of Incompressible and Pairwise Incompressible Surfaces in Knot Complements

本文主要利用链环补空间中曲面拓扑图的性质来研究一类链环L(n,3)(n∈Z^(+))补空间中处于标准位置的不可压缩且配对不可压缩曲面F的性质,进而得到曲面F的特征数.首先,根据纽结的性质,对一类链环L(n,3)进行研究,给出这类链环的分类,然后对于标准化后的链环L(n,3),如果F■S^(3)-L(n,3)为不可压缩且配对不可压缩曲面,则F为穿孔球面.

In this paper,we mainly study a class of incompressible and pairwise incompressible surface F which in the complement of link L(n,3)(n∈Z^(+))by using the properties of topological graph of F.Furthermore,the properties of the surface characteristic number are obtained.We study properties of link L(n,3)by the properties of knots and give classifications for the links.Suppose that L(n,3)is a normalized link,and F■S^(3)-L is an incompressible and pairwise incompressible surface.We prove that F is a punctured sphere.