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Seifert fibrations of lens spaces

  • Hansjörg Geiges
  • Christian Lange
Article

Abstract

We classify the Seifert fibrations of any given lens space L(pq). Starting from any pair of coprime non-zero integers \(\alpha _1^0,\alpha _2^0\), we give an algorithmic construction of a Seifert fibration \(L(p,q)\rightarrow S^2(\alpha |\alpha _1^0|,\alpha |\alpha _2^0|)\), where the natural number \(\alpha \) is determined by the algorithm. This algorithm produces all possible Seifert fibrations, and the isomorphisms between the resulting Seifert fibrations are described completely. Also, we show that all Seifert fibrations are isomorphic to certain standard models.

Keywords

Seifert fibration Seifert invariants Lens space 3-manifold 

Mathematics Subject Classification

57M50 55R65 57M10 57M60 

Notes

Acknowledgements

We thank the referee for useful comments that helped to improve the exposition.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnCologneGermany

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