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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
DOI: https://doi.org/10.1090/S0002-9939-1985-0781077-2
MathSciNet review: 781077
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0781077-2
Keywords: Proper map, proper embedding, loop theorem, plane
Article copyright: © Copyright 1985 American Mathematical Society

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