Geometrization of 3-dimensional orbifolds

Abstract

This paper is devoted to the proof of the orbifold theorem: If $\mathcal{O}$ is a compact connected orientable irreducible and topologically atoroidal $3$-orbifold with nonempty ramification locus, then $\mathcal{O}$ is geometric (i.e. has a metric of constant curvature or is Seifert fibred). As a corollary, any smooth orientation-preserving nonfree finite group action on $S^3$ is conjugate to an orthogonal action.