On properly embedding planes in 3-manifolds

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

doi:10.1090/S0002-9939-1976-0397735-2

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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

Proc. Amer. Math. Soc. 55 (1976), 461-464 Request permission

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.

References

E. M. Brown and T. W. Tucker, On proper homotopy theory for noncompact $3$-manifolds, Trans. Amer. Math. Soc. 188 (1974), 105–126. MR 334225, DOI 10.1090/S0002-9947-1974-0334225-X
David W. Henderson, Extensions of Dehn’s lemma and the loop theorem, Trans. Amer. Math. Soc. 120 (1965), 448–469. MR 187233, DOI 10.1090/S0002-9947-1965-0187233-0
John Stallings, On the loop theorem, Ann. of Math. (2) 72 (1960), 12–19. MR 121796, DOI 10.2307/1970146

Additional Information

Journal: Proc. Amer. Math. Soc. 55 (1976), 461-464
DOI: https://doi.org/10.1090/S0002-9939-1976-0397735-2
MathSciNet review: 0397735