Geometrization of 3-dimensional orbifolds

By M. Boileau, B. Leeb, J. Porti. 2000

186 citations recorded by the source corpus.

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 S3 is conjugate to an orthogonal action.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2423a93c844b04b35995da0f5df3191169aef0c9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. J. Porti
2. B. Leeb
3. Jonathan Dinkelbach
4. J. Lott
5. Bruce Kleiner
6. S. Maillot
7. M. Boileau
8. François Guéritaud

In Geometry and Topology

1. J. Porti
2. B. Leeb
3. Anna Wienhard
4. Bruce Kleiner
5. J. Lott
6. A. Iozzi
7. Jonathan Dinkelbach
8. S. Maillot

In Mathematical Physics

1. B. Leeb
2. J. Porti
3. Jonathan Dinkelbach
4. J. Lott
5. Anna Wienhard
6. Bruce Kleiner
7. A. Iozzi
8. M. Burger

Citations in the corpus

• Geometrization of Three-Dimensional Orbifolds via Ricci Flow (2011, methodology): “At that point, the additional effort required to deal with general orbifolds is relatively minor in comparison to the proof in [4].”
• Three-Dimensional Orbifolds and Their Geometric Structures (2003, methodology): “Recently in 2000, two different proofs were worked out, see [16, 17] and [43].”
• Geometrisation of 3-Manifolds (2010, result): “1 since we do not assume that M admits a geometric decomposition! Hence we need a trick similar to those of [9] and [7], which we now explain.”
• Angled decompositions of arborescent link complements (2006, background): “ted the case where P has incompressible boundary. Finally, when all angles are of the form π/n with n ≥ 2, the conjecture follows by a doubling argument from the hyperbolization theorem for orbifolds [3, 5]. We also note that the converse statement (that the ideal polyhedron P˜ must satisfy (1)–(3))”
• Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds (2008, methodology): “For orientation preserving non-free actions, they have been proven by Boileau, Leeb and Porti [2] along the lines suggested by Thurston [31] and based on Thurston’s Hyperbolization Theorem for Haken manifolds, using techniques from 3–dimensional topology, the deformation theory of geometric structur”
• Isometric Embeddings in Bounded Cohomology (2013, background): “Furthermore, without aiming at being exhaustive, here we just mention that Gromov Additivity Theorem has been also exploited in studying the possible degrees of maps between manifolds [42, 49, 17, 8, 18, 19], in establishing results about the behavior of manifolds under collapse [7, 5], and in vario”