Geodesic
Degree-one maps of Seifert manifolds into the Poincar\'e homology sphere
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 173-183

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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. 
@article{FPM_2005_11_4_a12,
     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},
     pages = {173--183},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a12/}
}
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A. A. Perfil'ev. Degree-one maps of Seifert manifolds into the Poincar\'e homology sphere. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 173-183. http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a12/