Geodesic
The Seifert Fiber Space Conjecture and Torus Theorem for Nonorientable 3-Manifolds
Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 482-489

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DOI

The Seifert-fiber-space conjecture for nonorientable 3-manifolds states that if M denotes a compact, irreducible, nonorientable 3-manifold that is not a fake P2 x S1 , if π1 M is infinite and does not contain Z 2 * Z 2 as a subgroup, and if π1 M does however contain a nontrivial, cyclic, normal subgroup, then M is a Seifert bundle. In this paper, we construct all compact, irreducible, nonorientable 3-manifolds (that do not contain a fake P2 × I) each of whose fundamental group contains Z 2 * Z 2 and an infinité cyclic, normal subgroup; none of these manifolds admits a Seifert fibration, but they satisfy Thurston's Geometrization Conjecture. We then reformulate the statement of the (nonorientable) SFS-conjecture and obtain a torus theorem for nonorientable manifolds.
DOI : 10.4153/CMB-1994-070-7
Mots-clés : Primary: 57N10, secondary: 57M50, Seifert bundle, Seifert bundle mod P 
Heil, Wolfgang; Whitten, Wilbur. The Seifert Fiber Space Conjecture and Torus Theorem for Nonorientable 3-Manifolds. Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 482-489. doi: 10.4153/CMB-1994-070-7
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     author = {Heil, Wolfgang and Whitten, Wilbur},
     title = {The {Seifert} {Fiber} {Space} {Conjecture} and {Torus} {Theorem} for {Nonorientable} {3-Manifolds}},
     journal = {Canadian mathematical bulletin},
     pages = {482--489},
     year = {1994},
     volume = {37},
     number = {4},
     doi = {10.4153/CMB-1994-070-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-070-7/}
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