On the diffeomorphism type of Seifert fibered spherical 3-orbifolds

TL;DR

This paper investigates the uniqueness of Seifert fibrations on spherical 3-orbifolds, providing a complete classification of the number of inequivalent fibrations and an algorithm to determine diffeomorphism between orbifolds.

Contribution

It characterizes the non-uniqueness of orbifold Seifert fibrations and offers a complete list and an algorithmic method for classification.

Findings

Finite number of fibrations (up to three) for certain orbifolds.

Complete classification of fibrations for all spherical Seifert orbifolds.

Algorithm to determine diffeomorphism between orbifolds with infinitely many fibrations.

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.