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| The Existence of a Meridional Curve in ClosedIncompressible Surfaces in Fully AlternatingLink Complements |
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Citation： |
Wei LIN.The Existence of a Meridional Curve in ClosedIncompressible Surfaces in Fully AlternatingLink Complements[J].Chinese Annals of Mathematics B,2024,45(1):73~80 |
| Page view： 335
Net amount： 300 |
Authors： |
Wei LIN; |
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| Abstract： |
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. |
Keywords： |
Fully alternating, Incompressible surfaces, Meridionally incompressible |
Classification： |
57M50, 57N75 |
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