## Essential embeddings of annuli and MĂ¶bius bands in $3$-manifolds

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- by James W. Cannon and C. D. Feustel
- Trans. Amer. Math. Soc.
**215**(1976), 219-239 - DOI: https://doi.org/10.1090/S0002-9947-1976-0391094-1
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## Abstract:

In this paper we give conditions when the existence of an â€śessentialâ€ť map of an annulus or MĂ¶bius band into a 3-manifold implies the existence of an â€śessentialâ€ť embedding of an annulus or MĂ¶bius band into that 3-manifold. Let ${\lambda _1}$ and ${\lambda _2}$ be disjoint simple â€śorientation reversingâ€ť loops in the boundary of a 3-manifold*M*and

*A*an annulus. Let $f:(A,\partial A) \to (M,\partial M)$ be a map such that ${f_\ast }:{\pi _1}(A) \to {\pi _1}(M)$ is monic and $f(\partial A) = {\lambda _1} \cup {\lambda _2}$. Then we show that there is an embedding $g:(A,\partial A) \to (M,\partial M)$ such that $g(\partial A) = {\lambda _1} \cup {\lambda _2}$.

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## Bibliographic Information

- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**215**(1976), 219-239 - MSC: Primary 57A10
- DOI: https://doi.org/10.1090/S0002-9947-1976-0391094-1
- MathSciNet review: 0391094