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