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

• Published in: Chinese annals of mathematics. Serie B Vol. 45; no. 1; pp. 73 - 80
• Main Author: Lin, Wei
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2024; Springer Nature B.V; School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,Liaoning,China
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; Toruses; Incompressible surfaces; Meridionally incompressible; 57M50; Fully alternating; 57N75
• ISSN: 0252-9599; 1860-6261
• DOI: 10.1007/s11401-024-0004-x

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 S 3 . 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 .