Geodesic
On Embedding Essential Annuli in M 3
Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1341-1350

Voir la notice de l'article provenant de la source Cambridge University Press

In [7; 8; 11] it is shown that an appropriate map of a planar surface into a 3-manifold can be replaced by an embedding. In [1 ; 4 ; 6 ; 7 ; 9 ; 10] conditions are given so that a "non-trivial" map of a planar surface (2-sphere) can be replaced by a non-trivial embedding of a planar surface (2-sphere). In this paper we give conditions on an annular map which guarantee the existence of a non-trivial embedding of an annulus. It is reported that F. Waldhausen has proved a similar but stronger "annulus theorem". 
Feustel, C. D. On Embedding Essential Annuli in M 3. Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1341-1350. doi: 10.4153/CJM-1974-127-x
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[1] 1. Epstein, D. B. A., Projective planes in 3-manifolds, Proc. London Math. Soc. 11 (1961), 469–484. Google Scholar

[2] 2. Daigle, R. J. and Feustel, C. D., Essential maps and embeddings in non-orientable M3 , Proc. Amer. Math. Soc. (to appear). Google Scholar

[3] 3. Feustel, C. D., Homotopic arcs are isotopic, Proc. Amer. Math. Soc. 17 (1966), 891–896. Google Scholar

[4] 4. Feustel, C. D., On embedding annuli in M3, Proc. Amer. Math. Soc. 35 (1972), 581–583. Google Scholar

[5] 5. Haken, W., Some results on surfaces in 3-manifolds, Studies in Modern Topology, Math. Assoc. Amer, (distributed by Prentice Hall, Englewood Cliffs, N.J., 1968), 39–98. Google Scholar

[6] 6. Papakyriakopoulos, C. D., On solid tori, Proc. London Math. Soc. 7 (1957), 281–299. Google Scholar

[7] 7. Papakyriakopoulos, C. D., On Dehn's lemma and the asphericity of knots, Ann. of Math. 66 (1957), 1–26. Google Scholar

[8] 8. Shapiro, A. and J. H. C. Whitehead, A proof and extension of Dehn's lemma, Bull. Amer. Math. Soc. 64 (1958), 174–178. Google Scholar

[9] 9. Stallings, J., On the loop theorem, Ann. of Math. 72 (1960), 12–19. Google Scholar

[10] 10. Whitehead, J. H. C., On 2-spheres in 3-manifolds, Bull. Amer. Math. Soc. 64 (1958), 161–166. Google Scholar

[11] 11. Waldhausen, F., Eine Verallgemeinerung des Schleifensatzes, Topology 6 (1967), 501–504. Google Scholar

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