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

被引：0
|
作者：
Lin, Wei [1 ]
机构：
[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Liaoning, Peoples R China
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2024年 / 45卷 / 01期
关键词：
Fully alternating; Incompressible surfaces; Meridionally incompressible;
D O I：
10.1007/s11401-024-0004-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in S3 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 subset of S x I L is an essential torus, then F contains a circle which is isotopic in S x 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 x I. If F subset of S x I \ L is a closed essential surface, then F contains a circle which is isotopic in S x I \ L to a meridian of L.
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页码：73 / 80
页数：8
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