Faessler, Daniel (2011): The Topology of locally volume collapsed 3-Orbifolds. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics |

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**DOI**: 10.5282/edoc.13185

### Abstract

In this thesis we study the geometry and topology of Riemannian 3-orbifolds which are locally volume collapsed with respect to a curvature scale. Our main result is that a sufficiently collapsed closed 3-orbifold without bad 2-suborbifolds satisﬁes Thurston’s Geometrization Conjecture. We also prove a version of this result with boundary. Kleiner and Lott indepedently and simultanously proved similar results ([KL11]). The main step of our proof is to construct a graph decomposition of sufficiently collapsed (closed) 3-orbifolds. We describe a coarse stratification of roughly 2-dimensional Alexandrov spaces which we then promote to a decomposition into suborbifolds for collapsed 3-orbifolds; this decomposition can then be reduced to a graph decomposition. We complete our proof by showing that graph orbifolds without bad 2-suborbifolds satisfy the Geometrization Conjecture.

Item Type: | Theses (Dissertation, LMU Munich) |
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Subjects: | 500 Natural sciences and mathematics > 510 Mathematics 500 Natural sciences and mathematics |

Faculties: | Faculty of Mathematics, Computer Science and Statistics |

Language: | English |

Date of oral examination: | 30. June 2011 |

1. Referee: | Leeb, Bernhard |

MD5 Checksum of the PDF-file: | 871c3cdd2ecb947d6637f000de4f153d |

Signature of the printed copy: | 0001/UMC 19556 |

ID Code: | 13185 |

Deposited On: | 07. Jul 2011 07:25 |

Last Modified: | 24. Oct 2020 03:43 |