Geometrization of 3-orbifolds of cyclic type:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Paris
Soc. Math. de France
2001
|
| Series: | Astérisque
272 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 208 S. graph. Darst. |
| ISBN: | 2856291007 |
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| 245 | 1 | 0 | |a Geometrization of 3-orbifolds of cyclic type |c Michel Boileau and Joan Porti |
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Record in the Search Index
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| adam_text | Titel: Geometrization of 3-orbifolds of cyclic type
Autor: Boileau, Michel
Jahr: 2001
CONTENTS
Introduction .................................................................. 1
1. Cone Manifolds .......................................................... 9
1.1. Basic Definitions ........................................................ 9
1.2. Sequences of hyperbolic cone 3-manifolds ............................................................11
2. Proof of Thurston s orbifold theorem for very good 3-orbifolds .... 15
2.1. Generalized Hyperbolic Dehn Filling ........................................................................15
2.2. The space of hyperbolic cone structures ................................................................16
2.3. Proof of Theorem 4 from Theorems A and B ........................................................19
2.4. Proof of Theorem 1 ........................................................................................................23
3. A compactness theorem for cone 3-manifolds
with cone angles bounded above by 7r ................................................................33
3.1. The Dirichlet polyhedron ............................................................................................34
3.2. Hausdorff-Gromov convergence for cone 3-manifolds ........................................39
3.3. Hausdorff-Gromov convergence implies geometric convergence....................41
3.4. Uniform lower bound for the cone-injectivity radius ........................................47
3.5. Some properties of geometric convergence ............................................................54
3.6. Cone 3-manifolds with totally geodesic boundary ............................................56
4. Local soul theorem for cone 3-manifolds
with cone angles less than or equal to 7r ............................................................61
4.1. Thurston s classification theorem of non-compact Euclidean
cone 3-manifolds ................................................................................................................63
4.2. Totally s-convex subsets in Euclidean cone 3-manifolds..................................65
4.3. Proof of the soul theorem ............................................................................................72
4.4. Proof of the local soul theorem..................................................................................75
4.5. Local soul theorem for cone 3-manifolds with boundary ................................77
5. Sequences of closed hyperbolic cone 3-manifolds
with cone angles less than 7r ........................................................................................79
5.1. The non-collapsing case ................................................................................................80
5.2. The collapsing case ..............................................................................................84
CONTENTS
5.3. Coverings a la Gromov ....................................................................................................86
5.4. From (e, £ )-Margulis coverings of abelian type to //-coverings
a la Gromov ........................................................................................................................63
5.5. (e, D)-Margulis neighborhood of thick turnover type ....................................98
6. Very good orbifolds and sequences of hyperbolic cone 3-manifolds .. 103
6.1. The non-collapsing case ................................................193
6.2. The collapsing case ......................................................196
6.3. From (e, D)-Margulis coverings of type a) and b) to //-coverings a la
Gromov ................................................................112
7. Uniformization of small 3-orbifolds ....................................119
7.1. Desingularization of ramified circle components ........................120
7.2. Uniformization of small 3-orbifolds with non-empty boundary ..........122
7.3. The sequence does not collapse ..........................................124
8. Haken 3-orbifolds ........................................................131
8.1. Proof of Thurston s Orbifold theorem ..................................132
8.2. Fundamental results on Haken 3-orbifolds ..............................132
8.3. Kleinian groups ........................................................136
8.4. Thurston s gluing theorem ..............................................140
8.5. Thurston s Fixed Point Theorem ........................................144
8.6. Thurston s Mirror Trick ................................................147
9. Examples ..................................................................159
9.1. A Euclidean collapse at angle ^ ........................................160
9.2. Another Euclidean collapse before 7r ....................................160
9.3. A Euclidean collapse at angle 7r ........................................161
9.4. Collapses at angle tt for Seifert fibred geometries ........................162
9.5. A collapse at 7r for Sol geometry ........................................164
9.6. An essential Euclidean turnover : opening of a cusp ....................166
9.7. A pillow ................................................................169
9.8. An incompressible RP2(7r, 7t) ............................................171
A. Limit of Hyperbolicity for Spherical 3-Orbifolds,
by Michael Heusener and Joan Porti ........................................173
A.l. Proof of the main proposition ..........................................175
B. Thurston s hyperbolic Delin filling Theorem ........................179
B.l. The manifold case ......................................................179
B.2. The orbifold case ......................................................187
B.3. Dehn filling with totally geodesic turnovers on the boundary..........194
Bibliography .....................
Index ..........................................................................207
ASTCRISQUIO 272
|
| any_adam_object | 1 |
| author | Boileau, Michel Porti, Joan 1967- |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T18:53:18Z |
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| isbn | 2856291007 |
| language | English |
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| spelling | Boileau, Michel Verfasser aut Geometrization of 3-orbifolds of cyclic type Michel Boileau and Joan Porti Paris Soc. Math. de France 2001 VI, 208 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Astérisque 272 Differentiaalmeetkunde gtt Topologische ruimten gtt Variétés à 3 dimensions Geometry, Differential Orbifolds Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd rswk-swf Orbifaltigkeit (DE-588)4667606-5 gnd rswk-swf Orbifaltigkeit (DE-588)4667606-5 s Dimension 3 (DE-588)4321722-9 s DE-604 Porti, Joan 1967- Verfasser (DE-588)173132189 aut Astérisque 272 (DE-604)BV002579439 272 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009479372&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boileau, Michel Porti, Joan 1967- Geometrization of 3-orbifolds of cyclic type Astérisque Differentiaalmeetkunde gtt Topologische ruimten gtt Variétés à 3 dimensions Geometry, Differential Orbifolds Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Orbifaltigkeit (DE-588)4667606-5 gnd |
| subject_GND | (DE-588)4321722-9 (DE-588)4667606-5 |
| title | Geometrization of 3-orbifolds of cyclic type |
| title_auth | Geometrization of 3-orbifolds of cyclic type |
| title_exact_search | Geometrization of 3-orbifolds of cyclic type |
| title_full | Geometrization of 3-orbifolds of cyclic type Michel Boileau and Joan Porti |
| title_fullStr | Geometrization of 3-orbifolds of cyclic type Michel Boileau and Joan Porti |
| title_full_unstemmed | Geometrization of 3-orbifolds of cyclic type Michel Boileau and Joan Porti |
| title_short | Geometrization of 3-orbifolds of cyclic type |
| title_sort | geometrization of 3 orbifolds of cyclic type |
| topic | Differentiaalmeetkunde gtt Topologische ruimten gtt Variétés à 3 dimensions Geometry, Differential Orbifolds Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Orbifaltigkeit (DE-588)4667606-5 gnd |
| topic_facet | Differentiaalmeetkunde Topologische ruimten Variétés à 3 dimensions Geometry, Differential Orbifolds Three-manifolds (Topology) Dimension 3 Orbifaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009479372&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
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