The multiple fibration problem for Seifert 3-orbifolds

TL;DR

This paper classifies all possible multiple fibrations of closed orientable Seifert 3-orbifolds across various geometries, extending previous work and providing geometric proofs for known computational results.

Contribution

It completes the classification of multiple fibrations for Seifert 3-orbifolds in geometries $\

Findings

Classified fibrations for $\

Confirmed previous computational results through geometric methods

Abstract

We conclude the multiple fibration problem for closed orientable Seifert three-orbifolds, namely the determination of all the inequivalent fibrations that such an orbifold may admit. We treat here geometric orbifolds with geometries $\mathbb R^3$ and $\mathbb S^2\times\mathbb R$ and bad orbifolds (hence non-geometric), since the only other geometry for which the multiple fibration phenomenon occurs, namely $\mathbb S^3$, has been treated before by the second and third author. For the geometry $\mathbb R^3$ we recover, by direct and geometric arguments, the computer-assisted results obtained by Conway, Delgado-Friedrichs, Huson and Thurston.