Local collapsing, orbifolds, and geometrization
This volume has two papers, which can be read separately. The first paper concerns local collapsing in Riemannian geometry. We prove that a three-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman without proof and was used in his proof of the geometrization conjecture. The second paper is about the geometrization of orbifolds. A three-dimensional closed orientable orbifold, which …
Read More ↓Title Statements
- Full title :Local collapsing, orbifolds, and geometrization / Bruce Kleiner, John Lott.
Summary
This volume has two papers, which can be read separately. The first paper concerns local collapsing in Riemannian geometry. We prove that a three-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman without proof and was used in his proof of the geometrization conjecture. The second paper is about the geometrization of orbifolds. A three-dimensional closed orientable orbifold, which has no bad suborbifolds, is known to have a geometric decomposition from work of Perelman in the manifold case, along with earlier work of Boileau-Leeb-Porti, Boileau-Maillot-Porti, Boileau-Porti, Cooper-Hodgson-Kerckhoff and Thurston. We give a new, logically independent, unified proof of the geometrization of orbifolds, using Ricci flow.--Provided by publisher.
Read More ↓Edition Statements
- Publication Date:©2014
Publication Statements
- Publisher(s):Société Mathématique de France
- Place of Publication:Paris
- Language:eng
- Publication Date:©2014
The Physical Object
- Description:177 pages : : illustrations ; : 24 cm.
Edition Identifiers
- ISBN:9782856297957, 2856297951
- oclc:ocn903163347
- LC Classification:QA671
- Dewey Decimal:516.373
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