# 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.

## Authors

Michel Boileau

Laboratoire Émile Picard
CNRS UMR 5580
Université Paul Sabatier
31062 Toulouse
France

Bernhard Leeb

Mathematisches Institut
Universität München
80333 München
Germany

Joan Porti

Departament de Matemàtiques
Universitat Autònoma de Barcelona
08193 Bellaterra
Spain