Foliations and the geometry of 3-manifolds:
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| Format: | Book |
| Language: | English |
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Oxford
Oxford Univ. Press
2007
|
| Edition: | 1. publ. |
| Series: | Oxford mathematical monographs
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 363 S. Ill., graph. Darst. |
| ISBN: | 9780198570080 0198570082 |
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| 245 | 1 | 0 | |a Foliations and the geometry of 3-manifolds |c Danny Calegari |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface vii
Acknowledgements x
1 Surface bundles 1
1.1 Surfaces and mapping class groups 1
1.2 Geometric structures on manifolds 7
1.3 Automorphisms of tori 9
1.4 PSL(2, Z) and Euclidean structures on tori 10
1.5 Geometric structures on mapping tori 11
1.6 Hyperbolic geometry 12
1.7 Geodesic laminations 17
1.8 Train tracks 32
1.9 Singular foliations 37
1.10 Quadratic holomorphic differentials 41
1.11 Pseudo Anosov automorphisms of surfaces 44
1.12 Geometric structures on general mapping tori 45
1.13 Peano curves 46
1.14 Laminations and pinching 48
2 The topology of S1 50
2.1 Laminations of S1 50
2.2 Monotone maps 54
2.3 Pullback of monotone maps 57
2.4 Pushforward of laminations 58
2.5 Left invariant orders 59
2.6 Circular orders 63
2.7 Homological characterization of circular groups 68
2.8 Bounded cohomology and Milnor Wood 74
2.9 Commutators and uniformly perfect groups 80
2.10 Rotation number and Ghys theorem 84
2.11 Homological characterization of laminations 87
2.12 Laminar groups 88
2.13 Groups with simple dynamics 90
2.14 Convergence groups 93
2.15 Examples 96
2.16 Analytic quality of groups acting on I and S1 105
xi
xii CONTENTS
3 Minimal surfaces 113
3.1 Connections, curvature 113
3.2 Mean curvature 116
3.3 Minimal surfaces in K3 119
3.4 The second fundamental form 121
3.5 Minimal surfaces and harmonic maps 123
3.6 Stable and least area surfaces 124
3.7 Existence theorems 130
3.8 Compactness theorems 132
3.9 Monotonicity and barrier surfaces 134
4 Taut foliations 137
4.1 Definition of foliations 137
4.2 Foliated bundles and holonomy 140
4.3 Basic constructions and examples 144
4.4 Volume preserving flows and dead ends 155
4.5 Calibrations 158
4.6 Novikov s theorem 161
4.7 Palmeira s theorem 168
4.8 Branching and distortion 172
4.9 Anosov flows 175
4.10 Foliations of circle bundles 178
4.11 Small Seifert fibered spaces 180
5 Finite depth foliations 183
5.1 Addition of surfaces 184
5.2 The Thurston norm on homology 185
5.3 Geometric inequalities and fibered faces 190
5.4 Sutured manifolds 193
5.5 Decomposing sutured manifolds 194
5.6 Constructing foliations from sutured hierarchies 197
5.7 Corollaries of Gabai s existence theorem 202
5.8 Disk decomposition and fibered links 204
6 Essential laminations 209
6.1 Abstract laminations 209
6.2 Essential laminations 212
6.3 Branched surfaces 214
6.4 Sink disks and Li s theorem 216
6.5 Dynamic branched surfaces 224
6.6 Pseudo Anosov flows 226
6.7 Push pull 232
6.8 Product covered flows 236
CONTENTS xiii
6.9 Genuine laminations 239
6.10 Small volume examples 242
7 Universal circles 246
7.1 Candel s theorem 246
7.2 Circle bundle at infinity 254
7.3 Separation constants 256
7.4 Markers 257
7.5 Leaf pocket theorem 261
7.6 Universal circles 263
7.7 Leftmost sections 264
7.8 Turning corners, and special sections 266
7.9 Circular orders 268
7.10 Examples 270
7.11 Special sections and cores 273
8 Constructing transverse laminations 274
8.1 Minimal quotients 274
8.2 Laminations of S niv 275
8.3 Branched surfaces and branched laminations 277
8.4 Straightening interstitial annuli 284
8.5 Genuine laminations and Anosov flows 289
9 Slitherings and other foliations 295
9.1 Slitherings 295
9.2 Eigenlaminations 298
9.3 Uniform and nonuniform foliations 302
9.4 The product structure on Eoo 305
9.5 Moduli of quadrilaterals 307
9.6 Constructing laminations 308
9.7 Foliations with one sided branching 310
9.8 Long markers 312
9.9 Complementary polygons 314
9.10 Pseudo Anosov flows 314
10 Peano curves 316
10.1 The Hilbert space H1/2 316
10.2 Universal Teichmuller space 318
10.3 Spaces of maps 321
10.4 Constructions and Examples 326
10.5 Moore s theorem 332
10.6 Quasigeodesic flows 332
10.7 Endpoint maps and equivalence relations 334
10.8 Construction of laminations 337
xiv CONTENTS
10.9 Quasigeodesic pseudo Anosov flows 338
10.10 Pseudo Anosov flows without perfect fits 340
10.11 Further directions 341
References 343
Index 357
|
| adam_txt |
CONTENTS
Preface vii
Acknowledgements x
1 Surface bundles 1
1.1 Surfaces and mapping class groups 1
1.2 Geometric structures on manifolds 7
1.3 Automorphisms of tori 9
1.4 PSL(2, Z) and Euclidean structures on tori 10
1.5 Geometric structures on mapping tori 11
1.6 Hyperbolic geometry 12
1.7 Geodesic laminations 17
1.8 Train tracks 32
1.9 Singular foliations 37
1.10 Quadratic holomorphic differentials 41
1.11 Pseudo Anosov automorphisms of surfaces 44
1.12 Geometric structures on general mapping tori 45
1.13 Peano curves 46
1.14 Laminations and pinching 48
2 The topology of S1 50
2.1 Laminations of S1 50
2.2 Monotone maps 54
2.3 Pullback of monotone maps 57
2.4 Pushforward of laminations 58
2.5 Left invariant orders 59
2.6 Circular orders 63
2.7 Homological characterization of circular groups 68
2.8 Bounded cohomology and Milnor Wood 74
2.9 Commutators and uniformly perfect groups 80
2.10 Rotation number and Ghys' theorem 84
2.11 Homological characterization of laminations 87
2.12 Laminar groups 88
2.13 Groups with simple dynamics 90
2.14 Convergence groups 93
2.15 Examples 96
2.16 Analytic quality of groups acting on I and S1 105
xi
xii CONTENTS
3 Minimal surfaces 113
3.1 Connections, curvature 113
3.2 Mean curvature 116
3.3 Minimal surfaces in K3 119
3.4 The second fundamental form 121
3.5 Minimal surfaces and harmonic maps 123
3.6 Stable and least area surfaces 124
3.7 Existence theorems 130
3.8 Compactness theorems 132
3.9 Monotonicity and barrier surfaces 134
4 Taut foliations 137
4.1 Definition of foliations 137
4.2 Foliated bundles and holonomy 140
4.3 Basic constructions and examples 144
4.4 Volume preserving flows and dead ends 155
4.5 Calibrations 158
4.6 Novikov's theorem 161
4.7 Palmeira's theorem 168
4.8 Branching and distortion 172
4.9 Anosov flows 175
4.10 Foliations of circle bundles 178
4.11 Small Seifert fibered spaces 180
5 Finite depth foliations 183
5.1 Addition of surfaces 184
5.2 The Thurston norm on homology 185
5.3 Geometric inequalities and fibered faces 190
5.4 Sutured manifolds 193
5.5 Decomposing sutured manifolds 194
5.6 Constructing foliations from sutured hierarchies 197
5.7 Corollaries of Gabai's existence theorem 202
5.8 Disk decomposition and fibered links 204
6 Essential laminations 209
6.1 Abstract laminations 209
6.2 Essential laminations 212
6.3 Branched surfaces 214
6.4 Sink disks and Li's theorem 216
6.5 Dynamic branched surfaces 224
6.6 Pseudo Anosov flows 226
6.7 Push pull 232
6.8 Product covered flows 236
CONTENTS xiii
6.9 Genuine laminations 239
6.10 Small volume examples 242
7 Universal circles 246
7.1 Candel's theorem 246
7.2 Circle bundle at infinity 254
7.3 Separation constants 256
7.4 Markers 257
7.5 Leaf pocket theorem 261
7.6 Universal circles 263
7.7 Leftmost sections 264
7.8 Turning corners, and special sections 266
7.9 Circular orders 268
7.10 Examples 270
7.11 Special sections and cores 273
8 Constructing transverse laminations 274
8.1 Minimal quotients 274
8.2 Laminations of S\niv 275
8.3 Branched surfaces and branched laminations 277
8.4 Straightening interstitial annuli 284
8.5 Genuine laminations and Anosov flows 289
9 Slitherings and other foliations 295
9.1 Slitherings 295
9.2 Eigenlaminations 298
9.3 Uniform and nonuniform foliations 302
9.4 The product structure on Eoo 305
9.5 Moduli of quadrilaterals 307
9.6 Constructing laminations 308
9.7 Foliations with one sided branching 310
9.8 Long markers 312
9.9 Complementary polygons 314
9.10 Pseudo Anosov flows 314
10 Peano curves 316
10.1 The Hilbert space H1/2 316
10.2 Universal Teichmuller space 318
10.3 Spaces of maps 321
10.4 Constructions and Examples 326
10.5 Moore's theorem 332
10.6 Quasigeodesic flows 332
10.7 Endpoint maps and equivalence relations 334
10.8 Construction of laminations 337
xiv CONTENTS
10.9 Quasigeodesic pseudo Anosov flows 338
10.10 Pseudo Anosov flows without perfect fits 340
10.11 Further directions 341
References 343
Index 357 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T17:14:16Z |
| indexdate | 2024-07-09T20:56:33Z |
| institution | BVB |
| isbn | 9780198570080 0198570082 |
| language | English |
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| spelling | Calegari, Danny Verfasser aut Foliations and the geometry of 3-manifolds Danny Calegari 1. publ. Oxford Oxford Univ. Press 2007 XIV, 363 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Foliations (Mathematics) Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Blätterung (DE-588)4007006-2 gnd rswk-swf Blätterung (DE-588)4007006-2 s Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015598691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Calegari, Danny Foliations and the geometry of 3-manifolds Foliations (Mathematics) Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Blätterung (DE-588)4007006-2 gnd |
| subject_GND | (DE-588)4321722-9 (DE-588)4037379-4 (DE-588)4007006-2 |
| title | Foliations and the geometry of 3-manifolds |
| title_auth | Foliations and the geometry of 3-manifolds |
| title_exact_search | Foliations and the geometry of 3-manifolds |
| title_exact_search_txtP | Foliations and the geometry of 3-manifolds |
| title_full | Foliations and the geometry of 3-manifolds Danny Calegari |
| title_fullStr | Foliations and the geometry of 3-manifolds Danny Calegari |
| title_full_unstemmed | Foliations and the geometry of 3-manifolds Danny Calegari |
| title_short | Foliations and the geometry of 3-manifolds |
| title_sort | foliations and the geometry of 3 manifolds |
| topic | Foliations (Mathematics) Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Blätterung (DE-588)4007006-2 gnd |
| topic_facet | Foliations (Mathematics) Three-manifolds (Topology) Dimension 3 Mannigfaltigkeit Blätterung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015598691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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