简单拓扑图及几乎交错链环补中的闭曲面  

Simple Topological Graph and Closed Surfaces in Almost Alternating Link Complements

作　　者：韩友发[1] 赵晓然 HAN Youfa;ZHAO Xiaoran(School of Mathematics,Liaoning Normal University,Dalian 116029,Liaoning,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《数学年刊（A辑）》2022年第1期57-72,共16页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11471151);辽宁省教育厅一般项目(No.LJ2019004)的资助。

摘　　要：研究了在曲面拓扑图的每个球泡中最多有一个鞍点的情况下,拓扑图的简单性与曲面亏格的关系.并利用正方形素方割的性质讨论了素、非分离几乎交错链环补空间中的闭、不可压缩、分段不可压缩曲面的性质.The authors discuss the relationship between the simplicity of the topological graph and the genus of the surface when there is at most one saddle in each bubble of the surface’s topological graph.And the properties of closed,incompressible and pairwise incompressible surfaces in prime,almost alternating link complements are discussed by using the properties of the prime dissection of a square.

关 键 词：简单拓扑图 分段不可压缩曲面 亏格 几乎交错链环 

分 类 号：O189.3[理学—数学]