Holomorphic curves in symplectic geometry:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Basel u.a.
Birkhäuser
1994
|
| Series: | Progress in mathematics
117 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 328 S. |
| ISBN: | 3764329971 0817629971 |
Staff View
MARC
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| 245 | 1 | 0 | |a Holomorphic curves in symplectic geometry |c Michèle Audin ... ed. |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1994 | |
| 300 | |a XI, 328 S. | ||
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Record in the Search Index
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| adam_text | Contents
Introduction: Applications of pseudo holomorphic curves
to symplectic topology
J. Lafontaine and M. Audin 1
1 Examples of problems and results in symplectic topology 1
2 Pseudo holomorphic curves in almost complex manifolds 3
3 Proofs of the symplectic rigidity results 9
4 What is in the book... and what is not 11
Bibliography 12
Part 1: Basic symplectic geometry
I An introduction to symplectic geometry
A. Banyaga 17
1 Linear symplectic geometry 17
2 Symplectic manifolds and vector bundles 21
Appendix: the Maslov class
M. Audin, A. Banyaga, F. Lalonde and L. Polterovich 33
Bibliography 39
II Symplectic and almost complex manifolds
M. Audin 41
1 Almost complex structures 41
2 Hirzebruch surfaces 50
3 Coadjoint orbits (of U(n)) 54
4 Symplectic reduction 58
5 Surgery? 62
Appendix: The canonical almost complex structure on the manifold of
1 jets of pseudo holomorphic mappings between two almost complex
manifolds P. Gauduchon 69
Bibliography 73
Part 2: Riemannian geometry and linear connections
III Some relevant Riemannian geometry
J. Lafontaine 77
1 Riemannian manifolds as metric spaces 77
2 The geodesic flow and its linearisation 87
3 Minimal manifolds 97
4 Two dimensional Riemannian manifolds 101
ix
5 An application to pseudo holomorphic curves 104
Appendix: the isoperimetric inequality
M. P. Muller 108
Bibliography Ill
IV Connexions lineaires, classes de Chern,
theoreme de Riemann Roch
P. Gauduchon 113
1 Connexions lineaires 113
2 Classes de Chern 126
3 Le theoreme de Riemann Roch 152
Bibliographie 161
Part 3: Pseudo holomorphic curves and applications
V Some properties of holomorphic curves
in almost complex manifolds
J. C. Sikorav 165
1 The equation df = g in C 166
2 Regularity of holomorphic curves 168
3 Other local properties 174
4 Properties of the area of holomorphic curves 178
5 Gromov s compactness theorem for holomorphic curves 183
Appendix: Stokes theorem for forms with differentiable coefficients .... 187
Bibliography 189
VI Singularities and positivity of intersections
of J holomorphic curves
D. McDuff 191
1 Elementary properties 192
2 Positivity of intersections 198
3 Local deformations 201
4 Perturbing away singularities 206
Appendix: The smoothness of the dependence on e
Gang Liu 212
Bibliography 215
VII Gromov s Schwarz lemma as an estimate of the gradient
for holomorphic curves
M. P. Muller 217
1 Introduction 217
2 A review of some classical Schwarz lemmas 217
3 Isoperimetric inequalities for J curves 218
x
4 The Schwarz and monotonicity lemmas 220
5 Continuous Lipschitz extension across a puncture 226
6 Higher derivatives 228
Bibliography 230
VIII Compactness
P. Prnisu 233
1 Riemann surfaces with nodes 234
2 Cusp curves 238
3 Proof of the compactness theorem 2.2.1 239
4 Convergence of parametrised curves 245
Bibliography 248
IX Exemples de courbes pseudo holomorphes
en geometrie riemannienne
F. Labourie 251
1 Immersions isometriques elliptiques 253
2 Courbure de Gauss prescrite 258
3 Autres exemples et constructions 261
Appendice: convergence d applications pseudo holomorphes 264
Bibliographie 268
X Symplectic rigidity: Lagrangian submanifolds
M. Audin, F. Lalonde and L. Polterovich 271
1 Lagrangian constructions 272
2 Symplectic area and Maslov classes—rigidity in split manifolds 284
3 Soft and hard Lagrangian obstructions to Lagrangian embeddings in C 293
4 Rigidity in cotangent bundles and applications to mechanics 297
5 Pseudo holomorphic curves: proof of the main rigidity theorem 307
Appendix: Exotic structures on R2 317
Bibliography 318
Index 323
Authors addresses 327
xi
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| isbn | 3764329971 0817629971 |
| language | English |
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| physical | XI, 328 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Holomorphic curves in symplectic geometry Michèle Audin ... ed. Basel u.a. Birkhäuser 1994 XI, 328 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 117 Fonctions holomorphes ram Variétés symplectiques ram Holomorphic functions Symplectic manifolds Holomorphe Kurve (DE-588)4160476-3 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 s Holomorphe Kurve (DE-588)4160476-3 s DE-604 Audin, Michèle 1954- Sonstige (DE-588)14151552X oth Progress in mathematics 117 (DE-604)BV000004120 117 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005552573&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holomorphic curves in symplectic geometry Progress in mathematics Fonctions holomorphes ram Variétés symplectiques ram Holomorphic functions Symplectic manifolds Holomorphe Kurve (DE-588)4160476-3 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| subject_GND | (DE-588)4160476-3 (DE-588)4194232-2 |
| title | Holomorphic curves in symplectic geometry |
| title_auth | Holomorphic curves in symplectic geometry |
| title_exact_search | Holomorphic curves in symplectic geometry |
| title_full | Holomorphic curves in symplectic geometry Michèle Audin ... ed. |
| title_fullStr | Holomorphic curves in symplectic geometry Michèle Audin ... ed. |
| title_full_unstemmed | Holomorphic curves in symplectic geometry Michèle Audin ... ed. |
| title_short | Holomorphic curves in symplectic geometry |
| title_sort | holomorphic curves in symplectic geometry |
| topic | Fonctions holomorphes ram Variétés symplectiques ram Holomorphic functions Symplectic manifolds Holomorphe Kurve (DE-588)4160476-3 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| topic_facet | Fonctions holomorphes Variétés symplectiques Holomorphic functions Symplectic manifolds Holomorphe Kurve Symplektische Geometrie |
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