On properly embedding planes in arbitrary 3-manifolds

Brown, E. M.; Feustel, C. D.

doi:10.1090/S0002-9939-1985-0781077-2

On properly embedding planes in arbitrary $3$-manifolds
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by E. M. Brown and C. D. Feustel

Proc. Amer. Math. Soc. 94 (1985), 173-178

DOI: https://doi.org/10.1090/S0002-9939-1985-0781077-2

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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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