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Matsumoto, Yukio and Montesinos Amilibia, José María
(1991)
*A proof of Thurston's uniformization theorem of geometric orbifolds.*
Tokyo Journal of Mathematics, 14
(1).
pp. 181-196.
ISSN 0387-3870

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Official URL: http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.tjm/1270130498

## Abstract

The authors prove that every geometric orbifold is good. More precisely, let X be a smooth connected manifold, and let G be a group of diffeomorphisms of X with the property that if any two elements of G agree on a nonempty open subset of X, then they coincide on X. If Q is an orbifold which is locally modelled on quotients of open subsets of X by finite subgroups of G, then the authors prove that the universal orbifold covering of Q is a (G,X)-manifold. A similar theorem was stated, and the proof sketched, in W. Thurston's lecture notes on the geometry and topology of 3-manifolds.

Item Type: | Article |
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Uncontrolled Keywords: | finite group action; orbifold covering; geometry |

Subjects: | Sciences > Mathematics > Topology Sciences > Mathematics > Geometry |

ID Code: | 22135 |

Deposited On: | 27 Jun 2013 17:00 |

Last Modified: | 12 Dec 2018 15:13 |

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