Fibered spherical 3-orbifolds

Abstract

In early 1930s Seifert and Threlfall classified up to conjugacy the finite subgroups of $\mathrm{SO}(4)$, this gives an algebraic classification of orientable spherical 3-orbifolds. For the most part, spherical 3-orbifolds are Seifert fibered. The underlying topological space and singular set of non-fibered spherical 3-orbifolds were described by Dunbar. In this paper we deal with the fibered case and in particular we give explicit formulae relating the finite subgroups of $\mathrm{SO}(4)$ with the invariants of the corresponding fibered 3-orbifolds. This allows to deduce directly from the algebraic classification topological properties of spherical 3-orbifolds.