Geometrization of 3-dimensional orbifolds

TL;DR

This paper proves the Orbifold Theorem for 3-orbifolds, establishing their geometric structure under certain conditions, and deduces that finite group actions on the 3-sphere are conjugate to orthogonal actions.

Contribution

It provides a proof of Thurston's Orbifold Theorem for 3-orbifolds, confirming their geometric nature and implications for group actions on spheres.

Findings

3-orbifolds with specified properties are geometric

Finite group actions on S^3 are conjugate to orthogonal actions

The proof confirms Thurston's announced theorem

Abstract

The purpose of this article is to give a proof of the Orbifold Theorem announced by Thurston in late 1981: If $O$ is a compact, connected, orientable, irreducible and topologically atoroidal 3-orbifold with non-empty ramification locus, then $O$ is geometric. As a corollary, any smooth orientation preserving non-free finite group action on $S^3$ is conjugate to an orthogonal action.