Geometrization of three-dimensional orbifolds via Ricci flow

Bruce Kleiner; John Lott

Geometrization of three-dimensional orbifolds via Ricci flow

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A three-dimensional closed orientable orbifold (with 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. Along the way we develop some tools for the geometry of orbifolds that may be of independent interest.

Original language	English (US)
Pages (from-to)	101-177
Number of pages	77
Journal	Asterisque
Issue number	365
State	Published - 2014

Keywords

Collapsing
Geometrization
Orbifold
Ricci flow

ASJC Scopus subject areas

General Mathematics

Cite this

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year = "2014",

language = "English (US)",

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AU - Lott, John

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N2 - A three-dimensional closed orientable orbifold (with 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. Along the way we develop some tools for the geometry of orbifolds that may be of independent interest.

AB - A three-dimensional closed orientable orbifold (with 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. Along the way we develop some tools for the geometry of orbifolds that may be of independent interest.

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KW - Geometrization

KW - Orbifold

KW - Ricci flow

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JO - Asterisque

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ER -

Geometrization of three-dimensional orbifolds via Ricci flow

Abstract

Keywords

ASJC Scopus subject areas

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