Immersions and Embeddings of Totally Geodesic Surfaces
Immersions and Embeddings of Totally Geodesic Surfaces
复制标题
全测地曲面的浸没和嵌入
DOI：
10.1112/blms/19.5.481
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发表时间：
1987
影响因子：
0.9
通讯作者：
D. Long
中科院分区：
文献类型：
--
作者：
D. Long
Waldhausen、Thurston 和其他人的工作表明，3 流形中存在封闭、可定向、不可压缩表面的嵌入对于理解该流形有很大帮助。不幸的是，存在许多不包含此类嵌入的流形示例。然而，至少在推测上，任何具有无限基本群的不可约流形都可能包含这样一个表面的浸没，这激发了对这样一个表面是否总是可以提升到 3-流形的某些有限覆盖中的嵌入问题的研究。一般性问题似乎距离解决还很遥远。本说明的目的是在非常特殊的情况下给出肯定的答案。
The work of Waldhausen, Thurston and others has shown that the existence of an embedding of a closed, orientable, incompressible surface in a 3-manifold is a great help in the understanding of that manifold. Unfortunately many examples exist of manifolds which contain no such embedding. However, it does seem at least conjecturally possible that any irreducible manifold with infinite fundamental group could contain an immersion of such a surface, and this has motivated the study of the question of whether such a surface can always be lifted to an embedding in some finite covering of the 3-manifold. The general question seems to be some way from resolution; the purpose of this note is to give an affirmative answer in a very special case.