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Immersions and Embeddings of Totally Geodesic Surfaces
Author(s) -
Long D. D.
Publication year - 1987
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/19.5.481
Subject(s) - geodesic , citation , mathematics , library science , combinatorics , computer science , geometry
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.