Geodesic
The Long Annulus Theorem
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 257-267

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DOI

Given a properly embedded incompressible surface F in a Haken manifold M, there is an integer n depending only on M and F with the following property: If there is a singular annulus in M that meets F in more then n nontrivial loops that are not freely homotopic on F then M contains an essential torus or annulus, or M is a bundle with fiber F, or M is a doubled twisted I-bundle with doubling surface F.
DOI : 10.4153/CMB-1986-040-4
Mots-clés : 57M99 
Evans, Benny. The Long Annulus Theorem. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 257-267. doi: 10.4153/CMB-1986-040-4
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     author = {Evans, Benny},
     title = {The {Long} {Annulus} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {257--267},
     year = {1986},
     volume = {29},
     number = {3},
     doi = {10.4153/CMB-1986-040-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-040-4/}
}
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