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Local collapsing, orbifolds, and geometrization / Bruce Kleiner and John Lott.

By: Kleiner, Bruce.
Contributor(s): Lott, John.
Material type: TextTextSeries: Asterisque ; 365.Publisher: Paris : Societe mathematique de France, 2014Description: 177 p. : illustrations ; 24 cm.ISBN: 9782856297957.Subject(s): Riemannian manifolds | Global differential geometry | Orbifolds | Three-manifolds (Topology) | Ricci flowDDC classification: 510=4
Contents:
Locally collapsed 3-manifolds -- Geometrization of three-dimensional orbifolds via Ricci flow-- References.
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
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Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
510=4 As853 (Browse shelf) Available C26467
Total holds: 0

Includes bibliographical references.

Locally collapsed 3-manifolds --
Geometrization of three-dimensional orbifolds via Ricci flow--
References.

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

In English; abstract also in French.

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