Abstract
We classify the Seifert fibrations of any given lens space L(p, q). 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.
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21 April 2021
A Correction to this paper has been published: https://doi.org/10.1007/s12188-021-00235-1
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We thank the referee for useful comments that helped to improve the exposition.
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Communicated by Janko Latschev.
The authors are partially supported by the SFB/TRR 191 ‘Symplectic Structures in Geometry, Algebra and Dynamics’.
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Geiges, H., Lange, C. Seifert fibrations of lens spaces. Abh. Math. Semin. Univ. Hambg. 88, 1–22 (2018). https://doi.org/10.1007/s12188-017-0188-z
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DOI: https://doi.org/10.1007/s12188-017-0188-z