Symplectic geometry and topology:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
1999
|
| Schriftenreihe: | Park City Mathematics Institute: IAS/Park City Mathematics Series
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 430 S. graph. Darst. |
| ISBN: | 0821808389 9780821840955 |
Internformat
MARC
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| 245 | 1 | 0 | |a Symplectic geometry and topology |c Yakov Eliashberg ..., eds. |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 1999 | |
| 300 | |a XIV, 430 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Park City Mathematics Institute: IAS/Park City Mathematics Series |v 7 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 0 | 7 | |a Topologie |0 (DE-588)4060425-1 |2 gnd |9 rswk-swf |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-3906-4 |
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Datensatz im Suchindex
| _version_ | 1805073780492468224 |
|---|---|
| adam_text |
Contents
Preface xiii
Introduction 1
Dusa McDuff, Introduction to Symplectic Topology 5
Introduction 7
Lecture 1. Basics 9
Existence of Many Symplectomorphisms 9
Linear Symplectic Geometry 10
The Cotangent Bundle 12
Lecture 2. Moser’s Argument 13
Lecture 3. The Linear Theory 17
^֊Compatible Almost Complex Structures 19
Vector Bundles 19
The Lagrangian Grassmannian 20
The Maslov Index 21
Lecture 4. The Nonsqueezing Theorem and Capacities 23
Preliminaries on J-Holomorphic Curves 26
Lecture 5. Sketch Proof of the Nonsqueezing Theorem 29
Fredholm Theory 30
Compactness 31
Bibliography 33
Helmut Hofer, Holomorphic Curves and Dynamics in Dimension
Three 35
Lecture 1. Problems, Basic Concepts and Overview 37
Periodic Orbits of Smooth Vector Fields on Three-Manifolds 37
Holomorphic Curves and Dynamics 43
Finer Aspects of Reeb Dynamics and Topology 46
Lecture 2. Analytical Tools 55
A Priori Estimates 55
Bubbling-off Analysis 58
Behaviour near a Puncture 59
vii
CONTENTS
viii
Lecture 3. The Weinstein Conjecture in the Overtwisted Case 67
An Explicit Local Bishop Family 67
The Implicit Function Theorem near an Embedded Disk 70
A Short Summary and the Prolongation of the Bishop Family 78
Lecture 4. The Weinstein Conjecture in the Tight Case 87
Sketch of the Proof 87
Global Uniqueness for Families of Pseudoholomorphic Disks 88
Lecture 5. Some Outlook 95
Bibliography 97
Michael Hutchings and Clifford Henry Taubes, An Introduction to
the Seiberg-Witten Equations on Symplectic Manifolds 103
Introduction 105
Lecture 1. Background from Differential Geometry 107
Vector Bundles 107
Connections 108
Metrics 110
Curvature 110
Self-Dual Two-Forms 111
Lecture 2. Spin and the Seiberg-Witten Equations 113
Principal Bundles and Associated Bundles 113
Spinc Structures 114
Some Group Theory 115
The Spinor Bundles 116
Clifford Multiplication 116
The Spin Connection 117
The Dirac Operator 118
The Seiberg-Witten Equations 118
Lecture 3. The Seiberg-Witten Invariants 121
Gauge Transformations 121
Basic Properties of the Moduli Space 122
Why the Conditions on b+7 123
Outline of the Proof of Compactness 123
The Seiberg-Witten Invariant 125
Examples and Applications 126
Lecture 4. The Symplectic Case, Part I 127
Statement of the Theorem 127
The Canonical Spin€ Structure 128
Step 1: Understanding the Dirac Equation 129
Step 2: Deforming the Curvature Equation 130
Step 3: Uniqueness of the Solution 131
Appendix: An Estimate on Beta 132
Lecture 5. The Symplectic Case, Part II 135
Summary of the Last Lecture 135
CONTENTS
ix
Motivation 136
Seiberg-Witten and Pseudoholomorphic Curves 136
Definition of the Gromov Invariant 137
Bibliography 141
Dietmar Salamon, Lectures on Floer Homology 143
Introduction 145
Lecture 1. Svmplectic Fixed Points and Morse Theory 147
The Arnold Conjecture 147
The Monotonicity Condition 149
The Morse֊Smale֊Witten Complex 150
Sympleetic Action 154
Connecting Orbits 155
Moduli Spaces 157
Lecture 2. Fredholm Theory 159
Fredholm Operators 159
The Linearized Operator 160
Lp-Estimates 161
The Conley-Zehnder Index 165
The Spectral Flow 166
Transversaiity 168
Exponential Convergence 170
Lecture 3. Floer Homology 173
Compactness 173
Floer Homology 176
Floer’s Gluing Theorem 179
Invariance of Floer Homology 181
A Natural Isomorphism 184
Calabi-Yau Manifolds 185
Novikov Rings 186
Floer Homology Revisited 187
Lecture 4. Gromov Compactness and Stable Maps 189
Bubbling 189
Soft Rescaling 191
Stable Maps 193
Deligne-Mumford Compactification 199
Lecture 5, Multi-Valued Perturbations 205
J-Holomorphic Spheres with Negative Chern Number 205
Multi-valued Perturbations 207
Local Slices 209
Branched Moduli Spaces 212
Perturbations and Stable Maps 218
Perturbations and Marked Points 219
Perturbations and Stable Maps 219
Compatibility 220
x CONTENTS
Rational Gromov-Witten Invariants 220
Rational Floer Homology 222
Bibliography 227
Alexander Givental, A Tutorial on Quantum Cohomology 231
Introduction 233
Lecture 1. Moduli Spaces of Stable Maps 237
Example: Quantum Cohomology of Complex Projective Spaces 237
Stable Maps 238
Lecture 2. Gromov-Witten Invariants 241
Lecture 3. QH*(G/B) and Quantum Toda Lattices 247
Lecture 4. Singularity Theory 253
Lecture 5. Toda Lattices and the Mirror Conjecture 259
Bibliography 263
Mikhail Grinberg and Robert MacPherson, Euler Characteristics
and Lagrangian Intersections 265
Introduction 267
Lecture 1. 269
The Centerpiece Theorem 269
Stratifications 269
Transversality 270
The Euler Characteristic of a Constructible Function 271
Homology O-Product of Cycles 272
The Characteristic Cycle in Dimension One 272
Lecture 2. 275
The Conormal Variety to a Stratification 275
Whitney Conditions 275
Generic Covectors 276
The Half-Link 277
The Characteristic Cycle 277
Signs 278
Lecture 3. 279
Classical Morse Theory 279
Stratified Morse Theory 280
Comments 281
Lecture 4. 283
Standard Pairs 283
Proof of Theorem 1.1: The General Case 284
Fáry Functors 285
CONTENTS xi
Lecture 5. 287
Fåry Functors: Comments and Examples 287
Monodromy 288
Euler Characteristics 289
Poincare-Verdier Duality 289
Morse Local Systems 290
Perverse Sheaves 290
Bibliography 293
Lisa C. Jeffrey, Hamiltonian Group Actions and Symplectic
Reduction 295
Lecture 1. Introduction to Hamiltonian Group Actions 297
Some Elementary Properties of Moment Maps 298
The Symplectic Quotient 299
The Normal Form Theorem 300
Lecture 2. The Geometry of the Moment Map 303
Convexity Theorems 303
The Moment Polytope 303
The Duistermaat-Heckman Theorem, Version I 304
Operations on Moment Polytopes 305
Symplectic Cutting 305
Toric Manifolds 306
Lecture 3. Equivariant Cohomology and the Cartan Model 309
The Cartan Model 310
Equivariant Characteristic Classes 310
The Abelian Localization Theorem 312
Lecture 4. The Duistermaat-Heckman Theorem and Applications to the
Cohomology of Symplectic Quotients 315
Stationary Phase Approximation 315
The Natural Map к : Hq(M) — H*(Mred) 316
Remarks on Quantization and Representation Theory 316
Nonabelian Localization 317
Lecture 5. Moduli Spaces of Vector Bundles over Riemann Surfaces 321
Prototype: The Jacobian 321
The Jacobian As an Infinite Dimensional Symplectic Quotient 322
The Moduli Space of Flat Connections on a Riemann Surface 323
The Line Bundle over the Moduli Space of Flat Connections 323
Exercises 325
Hamiltonian group actions and symplectic reduction: Exercise 1 (Lectures
1 and 2) 325
Exercise 2 (Lectures 3-5) 328
Bibliography
331
xii
CONTENTS
Jerrold E. Marsden, Park City Lectures on Mechanics, Dynamics,
and Symmetry 335
Introduction 337
Lecture 1. Reduction for Mechanical Systems with Symmetry 339
Lecture 2. Stability, Underwater Vehicle Dynamics and Phases 353
Lecture 3. Systems with Rolling Constraints and Locomotion 373
Lecture 4. Optimal Control and Stabilization of Balance Systems 385
Lecture 5. Variational Integrators 395
Bibliography 413 |
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| genre_facet | Konferenzschrift 1997 Park City Utah |
| id | DE-604.BV012808815 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T05:15:03Z |
| institution | BVB |
| isbn | 0821808389 9780821840955 |
| language | English |
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| physical | XIV, 430 S. graph. Darst. |
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| spelling | Symplectic geometry and topology Yakov Eliashberg ..., eds. Providence, R.I. American Mathematical Society 1999 XIV, 430 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Park City Mathematics Institute: IAS/Park City Mathematics Series 7 Hier auch später erschienene, unveränderte Nachdrucke Topologie (DE-588)4060425-1 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1997 Park City Utah gnd-content Symplektische Geometrie (DE-588)4194232-2 s Topologie (DE-588)4060425-1 s DE-604 Ēlîʾašberg, Yaʿaqov 1946- Sonstige (DE-588)113721544 oth Erscheint auch als Online-Ausgabe 978-1-4704-3906-4 Park City Mathematics Institute: IAS/Park City Mathematics Series 7 (DE-604)BV010402400 7 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008711881&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Symplectic geometry and topology Park City Mathematics Institute: IAS/Park City Mathematics Series Topologie (DE-588)4060425-1 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4194232-2 (DE-588)1071861417 |
| title | Symplectic geometry and topology |
| title_auth | Symplectic geometry and topology |
| title_exact_search | Symplectic geometry and topology |
| title_full | Symplectic geometry and topology Yakov Eliashberg ..., eds. |
| title_fullStr | Symplectic geometry and topology Yakov Eliashberg ..., eds. |
| title_full_unstemmed | Symplectic geometry and topology Yakov Eliashberg ..., eds. |
| title_short | Symplectic geometry and topology |
| title_sort | symplectic geometry and topology |
| topic | Topologie (DE-588)4060425-1 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| topic_facet | Topologie Symplektische Geometrie Konferenzschrift 1997 Park City Utah |
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