Geodesic
Degree-one maps of Seifert manifolds into the Poincaré homology sphere
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 173-183 
A. A. Perfil'ev. Degree-one maps of Seifert manifolds into the Poincaré homology sphere. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 173-183. http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a12/
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     author = {A. A. Perfil'ev},
     title = {Degree-one maps of {Seifert} manifolds into the {Poincar\'e} homology sphere},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to the Legrand–Wang–Zieschang problem of minimal (in the sense of degree-one maps) Seifert manifolds. The main result is that the set of all possible map degrees from a Seifert manifold to a manifold with a finite fundamental group whose base is a sphere or a torus depends only on residues of parameters of exceptional fibers of the Seifert manifold. The minimality of some Seifert manifolds is proved by using this theorem.

[1] Matveev S. V., Perfilev A. A., “Periodichnost stepenei otobrazhenii mezhdu mnogoobraziyami Zeiferta”, Dokl. RAN, 395:4 (2004), 449–451 | MR

[2] Hayat-Legrand C., Matveev S., Zieschang H., “Computer calculation of the degree of maps into the Poincaré homology sphere”, Experiment. Math., 10:4 (2001), 497–508 | MR | Zbl

[3] Hayat-Legrand C., Wang S., Zieschang H., “Minimal Seifert manifolds”, Math. Ann, 308:4 (1997), 673–700 | DOI | MR | Zbl