一类二桥结补中本质曲面的性质

Properties of essential surface in the complement of a kind of 2-bridge knot.

设K是一类只含扭转的二桥结(即纽结投影图不含单一交叉点),通过对这一类纽结补中的本质曲面F与纽结交点对应的bubbles相交的所有可能情况进行分析,得到如果本质曲面F对应的拓扑图T(F)是简单的,便可得到曲面的亏格为零,并且进一步给出了不论本质曲面F对应的拓扑图T(F)是否简单,都可经过讨论曲线的不同穿越形式得到曲面F是穿孔球面.

It mainly discusses the properties of essential surface in knot complement by twisting-crossing number.Let K be a knid of 2-bridge with twisting index more than 1,and let F be an essential surface in S3-K.Then if the topological graph of F is simple,the genus of F is zero,furthermore,F is a punctured 2-sphere either the topological graph of F is simple or not by discussing the different cases of F∩S2±.