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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On properly embedding planes in arbitrary $ 3$-manifolds


Authors: E. M. Brown and C. D. Feustel
Journal: Proc. Amer. Math. Soc. 94 (1985), 173-178
MSC: Primary 57M35; Secondary 57N10
MathSciNet review: 781077
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Abstract: We prove an analog of the loop theorem for an arbitrary noncompact $ 3$-manifold. In particular, we show that the existence of a "nontrivial" proper map of a plane into a $ 3$-manifold implies the existence of a nearby nontrivial embedding of a plane into the $ 3$-manifold.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0781077-2
PII: S 0002-9939(1985)0781077-2
Keywords: Proper map, proper embedding, loop theorem, plane
Article copyright: © Copyright 1985 American Mathematical Society