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Degree-one maps of Seifert manifolds into the Poincaré homology sphere

Abstract

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.

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References

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 173–183, 2005.

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Perfilyev, A.A. Degree-one maps of Seifert manifolds into the Poincaré homology sphere. J Math Sci 144, 4484–4491 (2007). https://doi.org/10.1007/s10958-007-0286-z

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Keywords

  • Manifold
  • Fundamental Group
  • Cellular Structure
  • Geometric Representation
  • Common Multiple