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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On properly embedding planes in $ 3$-manifolds


Authors: E. M. Brown, M. S. Brown and C. D. Feustel
Journal: Proc. Amer. Math. Soc. 55 (1976), 461-464
DOI: https://doi.org/10.1090/S0002-9939-1976-0397735-2
MathSciNet review: 0397735
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Abstract: In this paper we prove an analog of the loop theorem for a certain class of noncompact $ 3$-manifolds. In particular, we show that the existence of a ``nontrivial'' proper map of a plane into a $ 3$-manifold implies the existence of a nontrivial proper embedding of a plane into a $ 3$-manifold.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0397735-2
Article copyright: © Copyright 1976 American Mathematical Society