Geometric theory of foliations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English German Portuguese |
| Published: |
Boston [u.a.]
Birkhäuser
1985
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Portug. übers. |
| Physical Description: | 205 S. |
| ISBN: | 0817631399 3764331399 |
Staff View
MARC
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| 100 | 1 | |a Camacho, César |d 1943- |e Verfasser |0 (DE-588)110369211 |4 aut | |
| 240 | 1 | 0 | |a Teoria geométrica das folheações |
| 245 | 1 | 0 | |a Geometric theory of foliations |c César Camacho ; Alcides Lins Neto |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1985 | |
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| 650 | 7 | |a Differentiaalmeetkunde |2 gtt | |
| 650 | 4 | |a Feuilletages (Mathématiques) | |
| 650 | 4 | |a Géométrie différentielle | |
| 650 | 4 | |a Foliations (Mathematics) | |
| 650 | 4 | |a Geometry, Differential | |
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Record in the Search Index
| _version_ | 1804115083855396864 |
|---|---|
| adam_text | CONTENTS
Introduction 1
Chapter I — Differentiable Manifolds
$1. Differentiable manifolds 5
§2. The derivative 13
§3. Immersions and submersions 14
§4 Submanifolds 16
§5. Regular values 17
§6. Transversality 17
§7. Partitions of unity 18
Chapter II — Foliations
$1. Foliations 21
§2. The leaves 31
§3. Distinguished maps 32
$4. Plane fields and foliations 35
§5. Orientation 36
§6. Orientable double coverings 37
$7. Orientable and transversely orientable foliations 38
Notes to Chapter II 41
Chapter III — The Topology of the Leaves
$1. The space of leaves 47
$2. Transverse uniformity 48
$3. Closed leaves 51
$4. Minimal sets of foliations 52
Notes to Chapter III 53
Chapter IV — Holonomy and the Stability Theorems
§1. Holonomy of a leaf 62
§2. Determination of the germ of a foliation in a 67
neighborhood of a leaf by the the holonomy
of the leaf
§3. Global trivialization lemma 69
§4. The local stability theorem 70
§5. Global stability theorem. Transversely orientable case 72
§6. Global stability theorem. General case 78
Notes to Chapter IV 80
Chapter V — Fiber Bundles and Foliations
$1. Fiber bundles 87
§2. Foliations transverse to the fibers of a fiber bundle 91
$3. The holonomy of 5 93
$4. Suspension of a representation 93
§5. Existence of germs of foliations 100
§6. Sacksteder s Example 102
Notes to Chapter V 106
Chapter VI — Analytic Foliations of Codimension One
$1. An outline of the proof of Theorem 1 116
§2. Singularities of maps /: R — 1R 118
§3. Haefliger s construction 121
J4. Foliations with singularities on D2 123
$5. The proof of Haefliger s theorem 127
Chapter VII Novikov s Theorem
$1. Sketch of the proof 131
$2. Vanishing cycles 133
$3. Simple vanishing cycles 138
$4. Existence of a compact leaf 140
$5. Existence of a Reeb component 149
$6. Other results of Novikov 152
$7. The non orientable case 157
Chapter VIII — Topological Aspects of the
Theory of Group Actions
$1. Elementary properties 159
$2. The theorem on the rank of S3 163
$3. Generalization of the rank theorem 165
§4. The Poincare Bendixson theorem for actions of R2 168
§5. Actions of the group of affine transformations 171
of the line
Appendix — Frobenius Theorem
§1. Vector fields and the Lie bracket 175
§2. Frobenius theorem 182
§3. Plane fields defined by differential forms 184
Exercises 189
Bibliography 199
Index 203
|
| any_adam_object | 1 |
| author | Camacho, César 1943- Lins Neto, Alcides 1947- |
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| dewey-full | 514/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.72 |
| dewey-search | 514/.72 |
| dewey-sort | 3514 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:16:59Z |
| institution | BVB |
| isbn | 0817631399 3764331399 |
| language | English German Portuguese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000396521 |
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| physical | 205 S. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
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| publisher | Birkhäuser |
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| spelling | Camacho, César 1943- Verfasser (DE-588)110369211 aut Teoria geométrica das folheações Geometric theory of foliations César Camacho ; Alcides Lins Neto Boston [u.a.] Birkhäuser 1985 205 S. txt rdacontent n rdamedia nc rdacarrier Aus d. Portug. übers. Differentiaalmeetkunde gtt Feuilletages (Mathématiques) Géométrie différentielle Foliations (Mathematics) Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Blätterung (DE-588)4007006-2 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Blätterung (DE-588)4007006-2 s DE-604 Geometrie (DE-588)4020236-7 s Lins Neto, Alcides 1947- Verfasser (DE-588)11036922X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000396521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Camacho, César 1943- Lins Neto, Alcides 1947- Geometric theory of foliations Differentiaalmeetkunde gtt Feuilletages (Mathématiques) Géométrie différentielle Foliations (Mathematics) Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Geometrie (DE-588)4020236-7 gnd Blätterung (DE-588)4007006-2 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4020236-7 (DE-588)4007006-2 |
| title | Geometric theory of foliations |
| title_alt | Teoria geométrica das folheações |
| title_auth | Geometric theory of foliations |
| title_exact_search | Geometric theory of foliations |
| title_full | Geometric theory of foliations César Camacho ; Alcides Lins Neto |
| title_fullStr | Geometric theory of foliations César Camacho ; Alcides Lins Neto |
| title_full_unstemmed | Geometric theory of foliations César Camacho ; Alcides Lins Neto |
| title_short | Geometric theory of foliations |
| title_sort | geometric theory of foliations |
| topic | Differentiaalmeetkunde gtt Feuilletages (Mathématiques) Géométrie différentielle Foliations (Mathematics) Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Geometrie (DE-588)4020236-7 gnd Blätterung (DE-588)4007006-2 gnd |
| topic_facet | Differentiaalmeetkunde Feuilletages (Mathématiques) Géométrie différentielle Foliations (Mathematics) Geometry, Differential Differentialgeometrie Geometrie Blätterung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000396521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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