Geometrization of 3-dimensional orbifolds

2005/07/01 by Michel Boileau, Bernhard Leeb, Joan Porti · 2 citations
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Orbifold #Mathematics #Fibered knot #Corollary #Pure mathematics #Locus (genetics) #Constant (computer programming) #Group action #Finite group #Group (periodic table)

paper · pdf · doi:10.4007/annals.2005.162.195

openalex publication_date 2005/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

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

Citations

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
• Three-manifolds with positive Ricci curvature
• Hyperbolic Structures on 3-manifolds, III: Deformations of 3-manifolds with incompressible boundary
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• The Geometries of 3-Manifolds

Cited by

• Deforming Euclidean cone 3–manifolds
• Orbifold [wikipedia]