The Existence of a Meridional Curve in Closed Incompressible Surfaces in Fully Alternating Link Complements  

The Existence of a Meridional Curve in Closed Incompressible Surfaces in Fully Alternating Link

作　　者：Wei LIN 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,Liaoning,China

出　　处：《Chinese Annals of Mathematics,Series B》2024年第1期73-80,共8页数学年刊（B辑英文版）

摘　　要：Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in S^(3) contains a circle isotopic in the link complement to a meridian of the links.Based on this result,he was able to argue the hyperbolicity of non-split prime alternating links in S3.Adams et al.showed that if F■S×I\L is an essential torus,then F contains a circle which is isotopic in S×I\L to a meridian of L.The author generalizes his result as follows:Let S be a closed orientable surface,L be a fully alternating link in S×I\If F ■ S×I\L is a closed essential surface,then F contains a circle which is isotopic in S×I\L to a meridian of L.

关 键 词：Fully alternating Incompressible surfaces Meridionally incompressible 

分 类 号：O186.11[理学—数学]