On the diffeomorphism type of Seifert fibered spherical 3-orbifolds

Mattia Mecchia; Andrea Seppi

doi:10.13137/2464-8728/30920

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arXiv · 2005.12023

On the diffeomorphism type of Seifert fibered spherical 3-orbifolds

Mattia Mecchia·Andrea Seppi

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Abstract

It is well known that, among closed spherical Seifert three-manifolds, only lens spaces and prism manifolds admit several Seifert fibrations which are not equivalent up to diffeomorphism. Moreover the former admit infinitely many fibrations, and the latter exactly two. In this work, we analyse the non-uniqueness phenomenon for orbifold Seifert fibrations. For any closed spherical Seifert three-orbifold, we determine the number of its inequivalent fibrations. When these are in a finite number (in fact, at most three) we provide a complete list. In case of infinitely many fibrations, we describe instead an algorithmic procedure to determine whether two closed spherical Seifert orbifolds are diffeomorphic.

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BibTeX RIS

Mattia Mecchia, Andrea Seppi. 2020-05-25. On the diffeomorphism type of Seifert fibered spherical 3-orbifolds. https://doi.org/10.13137/2464-8728/30920

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