交错环链补中不可压缩曲面的性质  

Properties of Incompressible Surfaces in Alternating Link Complements

作　　者：韩友发[1] 赵岩[1] 杨盛武[1] 

机构地区：[1]辽宁师范大学数学学院数学系,大连116029

出　　处：《吉林大学学报（理学版）》2005年第1期16-19,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10171024);辽宁师范大学资助项目基金(批准号:202202).

摘　　要：设L是S3中的一个交错环链,将L投影到S2上,L的每个交叉点都对应一个bubble,用来体现L的交叉点性质.如果L有n个交叉点,则投影图就有n个bubble与之对应,从而在S3中构造了2个二维球面S2+和S2-.设F是S3-L中的不可压缩、分段不可压缩曲面,并且处于一般位置,则F∩S2±是一组简单闭曲线.通过讨论F∩S2±的性质刻画了曲面的性质.当F∩S2±的图(也称为拓扑图)是特殊简单的,则曲面F的亏格是零.Let L be an alternating link in S^3 and let L project on S^2 except near crossings of L where L lies on a bubble. If the projective diagram on S^2 has n crossings, then there are n bubbles. Thus are construced (2-spheres) surfaces S^2_+ and S^2_- by the properties of the link. Let F be an incompressible and pairwise incompressible surface in S^3-L, there is a collection of simple closed curves when the surface F is in a standard (position). The surfaces are described by discussing the properties of F∩S^2_±. The genus of the surface equals zero if the graph of F∩S^2_± is special simple.

关 键 词：交错环链 亏格 不可压缩曲面 

分 类 号：O189.3[理学—数学]