**Astérisque**

Volume: 365;
2014;
177 pp;
Softcover

MSC: Primary 53; 57;
**Print ISBN: 978-2-85629-795-7
Product Code: AST/365**

List Price: $67.00

Individual Member Price: $53.60

# Local Collapsing, Orbifolds, and Geometrization

Share this page
*Bruce Kleiner; John Lott*

A publication of the Société Mathématique de France

This volume has two papers which can be read separately. The first paper concerns local collapsing in Riemannian geometry. The authors 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. This is known from the 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. The authors give a new, logically independent, unified proof of the geometrization of orbifolds, using Ricci flow.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Table of Contents

# Table of Contents

## Local Collapsing, Orbifolds, and Geometrization

#### Readership

Graduate students and research mathematicians interested in collapsing, orbifolds, and geometrization.