The hyperbolization theorem for fibered 3-manifolds:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch Französisch |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2001
|
| Schriftenreihe: | Société Mathématique de France: SMF AMS texts and monographs
7 Astérisque 235 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009704722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 126 S. graph. Darst. |
| ISBN: | 0821821539 |
Internformat
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| 240 | 1 | 0 | |a Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3 |
| 245 | 1 | 0 | |a The hyperbolization theorem for fibered 3-manifolds |c Jean-Pierre Otal |
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Datensatz im Suchindex
| _version_ | 1819384447177326592 |
|---|---|
| adam_text | Contents
Introduction ix
Chapter 1. Tcichmiiller Spaces and Kleinian Groups 1
1.1. Hyperbolic Space 1
1.2. Quasiconformal Homeomorphisms 6
1.3. Teichnriiller Space; the Space of Quasi Fuchsian Groups 9
1.4. Thurston s Compactification of Teichrmiller Space 12
1.5. Classification of the Elements of .Mod(S) 14
Chapter 2. Real Trees and Degenerations of Hyperbolic Structures 17
2.1. Real Trees 17
2.2. Real Trees and Degenerations of Actions on Hyperbolic Space 21
2.3. Actions with Small Arc Stabilizers of Fuchsian Groups on Real Trees 29
Chapter 3. Geodesic Laminations and Real Trees 33
3.1. Realization of a Geodesic Lamination in a Real Tree 33
3.2. Proof of Theorem 3.1.4 37
Chapter 4. Geodesic Laminations and the Gromov Topology 41
4.1. Realization of a Train Track in a Hyperbolic Manifold 42
4.2. Conclusion of the Proof of Theorem 4.0.1 48
4.3. Proof of Lemma 4.2.2 50
Chapter 5. The Double Limit Theorem 53
5.1. The Ahlfors Lemma 54
5.2. A Convergence Criterion in the Space of Quasi Fuchsian Groups 56
Chapter 6. The Hyperbolization Theorem for Fibered Manifolds 59
6.1. Construction of a Representation of the Subgroup tti(S) 59
6.2. Study of the Limit Set of the Representation p^ 61
6.3. Construction of a Representation of the Group tt (M0) 69
6.4. Proof of the Hyperbolization Theorem for Fibered Manifolds 71
Chapter 7. Sullivan s Theorem 75
7.1. Decomposition of the Action of a Group into a Conservative and a
Dissipative Part 75
7.2. The Action of a Kleinian Group on a Conservative Borel Set 78
7.3. Proof of Sullivan s Theorem 82
Chapter 8. Actions of Surface Groups on Real Trees 85
8.1. Construction of a Transverse Map 85
8.2. Construction of a Dual Tree 93
vii
viii CONTENTS
8.3. Construction of a Measured Geodesic Lamination 98
8.4. Proof of Theorem 8.1.1. 99
Chapter 9. Two Examples of Hyperbolic Manifolds That Fiber over the Circle 105
9.1. The Gieseking Manifold 105
9.2. The Right Angled Regular Dodecahedron 108
Appendix. Geodesic Laminations 109
A.I. Geodesic Laminations 109
A.2. The Geometry of the Complement of a Geodesic Lamination 112
A.3. Measured Geodesic Laminations 114
Bibliography 121
Index 125
|
| any_adam_object | 1 |
| author | Otal, Jean-Pierre |
| author_facet | Otal, Jean-Pierre |
| author_role | aut |
| author_sort | Otal, Jean-Pierre |
| author_variant | j p o jpo |
| building | Verbundindex |
| bvnumber | BV014158996 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.4 |
| callnumber-search | QA612.4 |
| callnumber-sort | QA 3612.4 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 832 SK 300 |
| ctrlnum | (OCoLC)47650708 (DE-599)BVBBV014158996 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014158996 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:00:22Z |
| institution | BVB |
| isbn | 0821821539 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009704722 |
| oclc_num | 47650708 |
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| owner_facet | DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-83 DE-11 |
| physical | XIV, 126 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Société Mathématique de France: SMF AMS texts and monographs Astérisque |
| series2 | Société Mathématique de France: SMF AMS texts and monographs Astérisque |
| spellingShingle | Otal, Jean-Pierre The hyperbolization theorem for fibered 3-manifolds Société Mathématique de France: SMF AMS texts and monographs Astérisque Geometry, Hyperbolic Group theory Low-dimensional topology Dimension 3 (DE-588)4321722-9 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd Variationsrechnung (DE-588)4062355-5 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd Hyperbolischer Raum (DE-588)4161046-5 gnd |
| subject_GND | (DE-588)4321722-9 (DE-588)4161041-6 (DE-588)4062355-5 (DE-588)4280826-1 (DE-588)4161046-5 |
| title | The hyperbolization theorem for fibered 3-manifolds |
| title_alt | Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3 |
| title_auth | The hyperbolization theorem for fibered 3-manifolds |
| title_exact_search | The hyperbolization theorem for fibered 3-manifolds |
| title_full | The hyperbolization theorem for fibered 3-manifolds Jean-Pierre Otal |
| title_fullStr | The hyperbolization theorem for fibered 3-manifolds Jean-Pierre Otal |
| title_full_unstemmed | The hyperbolization theorem for fibered 3-manifolds Jean-Pierre Otal |
| title_short | The hyperbolization theorem for fibered 3-manifolds |
| title_sort | the hyperbolization theorem for fibered 3 manifolds |
| topic | Geometry, Hyperbolic Group theory Low-dimensional topology Dimension 3 (DE-588)4321722-9 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd Variationsrechnung (DE-588)4062355-5 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd Hyperbolischer Raum (DE-588)4161046-5 gnd |
| topic_facet | Geometry, Hyperbolic Group theory Low-dimensional topology Dimension 3 Hyperbolische Geometrie Variationsrechnung Niederdimensionale Topologie Hyperbolischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009704722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT otaljeanpierre letheoremedhyperbolisationpourlesvarietesfibreesdedimension3 AT otaljeanpierre thehyperbolizationtheoremforfibered3manifolds |