CAJ | 학술논문

通过对非简单拓扑图的性质进行讨论，研究了纽结补中的不可压缩、分段不可压缩曲面的性质。通过拓扑图的特征数给出了这些曲面亏格的性质，同时对不可压缩、分段不可压缩曲面的分支数与非简单拓扑图的非最内环道的字表示间的关系进行了研究。设曲面 S? S3－K是不可压缩、分段不可压缩曲面，S2±是二维球面，给出了拓扑图每条闭曲线C字的表示w ±（C），这些字母有 P ，S ，它们描述了曲面的分支数和bubbles的相交，证明了当 S∩ S2±的图（即拓扑图）的分支数等于3时，若拓扑图是非简单的，那么非简单拓扑图有唯一的形式，并通过单位拓扑图给出它们的表示，从而得到拓扑图的特征数是2，进而曲面 S的亏格等于0（这里 S是纽结补中的本质曲面）。
통과대비간단탁복도적성질진행토론，연구료뉴결보중적불가압축、분단불가압축곡면적성질。통과탁복도적특정수급출료저사곡면우격적성질，동시대불가압축、분단불가압축곡면적분지수여비간단탁복도적비최내배도적자표시간적관계진행료연구。설곡면 S? S3－K시불가압축、분단불가압축곡면，S2±시이유구면，급출료탁복도매조폐곡선C자적표시w ±（C），저사자모유 P ，S ，타문묘술료곡면적분지수화bubbles적상교，증명료당 S∩ S2±적도（즉탁복도）적분지수등우3시，약탁복도시비간단적，나요비간단탁복도유유일적형식，병통과단위탁복도급출타문적표시，종이득도탁복도적특정수시2，진이곡면 S적우격등우0（저리 S시뉴결보중적본질곡면）。
In this paper ,we deal with incompressible pairwise incompressible surfaces in link comple‐ments by studying the properties of non‐simple topological graph .We give the properties of genus by using the characteristics number .We discuss the relation betw een the boundary components number of essential surfaces and the words of loops in non‐simple topological graph .Let S? S3 -K be incom‐pressible pairwise incompressible surface and let S2± be 2‐sphere .Each component C of S∩ S2± can be associated a cyclic word w± (C) in letter P(= puncture) and S(= saddle) ,which records ,in order , the intersections of C with K and with the bubbles ,respectively .We give the properties of non‐sim‐ple topological graph by making use of definitions ,theorems and properties of the topological graph , essential surfaces in link complements .One can know that the topological graph with three compo‐nents has a unique form .We prove that the characteristic number of the topological graph is two and the genus of the essential surface equals zero if the topological graph is non‐simple and the component number of non‐simple topological graph S∩ S2± is three .