Essential embeddings of annuli and Möbius bands in 3-manifolds
| Autor: | James W. Cannon, C. D. Feustel |
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| Rok vydání: | 1976 |
| Předmět: | |
| Zdroj: | Transactions of the American Mathematical Society. 215:219-239 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/s0002-9947-1976-0391094-1 |
| Popis: | In this paper we give conditions when the existence of an “essential” map of an annulus or Möbius band into a 3-manifold implies the existence of an “essential” embedding of an annulus or Möbius band into that 3-manifold. Let λ 1 {\lambda _1} and λ 2 {\lambda _2} be disjoint simple “orientation reversing” loops in the boundary of a 3-manifold M and A an annulus. Let f : ( A , ∂ A ) → ( M , ∂ M ) f:(A,\partial A) \to (M,\partial M) be a map such that f ∗ : π 1 ( A ) → π 1 ( M ) {f_\ast }:{\pi _1}(A) \to {\pi _1}(M) is monic and f ( ∂ A ) = λ 1 ∪ λ 2 f(\partial A) = {\lambda _1} \cup {\lambda _2} . Then we show that there is an embedding g : ( A , ∂ A ) → ( M , ∂ M ) g:(A,\partial A) \to (M,\partial M) such that g ( ∂ A ) = λ 1 ∪ λ 2 g(\partial A) = {\lambda _1} \cup {\lambda _2} . |
| Databáze: | OpenAIRE |
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