Notes on Seiberg-Witten theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2000
|
| Series: | Graduate studies in mathematics
28 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 484 S. graph. Darst. |
| ISBN: | 9780821821459 0821821458 |
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MARC
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| 100 | 1 | |a Nicolaescu, Liviu I. |d 1964- |e Verfasser |0 (DE-588)124402887 |4 aut | |
| 245 | 1 | 0 | |a Notes on Seiberg-Witten theory |c Liviu I. Nicolaescu |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2000 | |
| 300 | |a XVIII, 484 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 28 | |
| 650 | 4 | |a Analyse globale (Mathématiques) | |
| 650 | 4 | |a Physique mathématique | |
| 650 | 4 | |a Seiberg-Witten, Invariants de | |
| 650 | 4 | |a Variétés topologiques à 4 dimensions | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Four-manifolds (Topology) | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Seiberg-Witten invariants | |
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Record in the Search Index
| _version_ | 1804128310028926977 |
|---|---|
| adam_text | Contents
Introduction xiii
Chapter 1. Preliminaries 1
§1.1. Bundles, connections and characteristic classes 1
1.1.1. Vector bundles and connections 1
1.1.2. Chern Weil theory 12
§1.2. Basic facts about elliptic equations 16
§1.3. Clifford algebras and Dirac operators 27
1.3.1. Clifford algebras and their representations 27
1.3.2. The Spin and Spirf groups 34
1.3.3. Spin and spirf structures 40
1.3.4. Dirac operators associated to spin and spirf structures 46
§1.4. Complex differential geometry 53
1.4.1. Elementary complex differential geometry 54
1.4.2. Cauchy Riemann operators 68
1.4.3. Dirac operators on almost Kahler manifolds 80
§1.5. Fredholm theory 85
1.5.1. Continuous families of elliptic operators 85
1.5.2. Genericity results 100
Chapter 2. The Seiberg Witten Invariants 103
§2.1. Seiberg Witten monopoles 103
ix
2.1.1. The Seiberg Witten equations 103
2.1.2. The functional set up 108
§2.2. The structure of the Seiberg Witten moduli spaces 114
2.2.1. The topology of the moduli spaces 114
2.2.2. The local structure of the moduli spaces 119
2.2.3. Generic smoothness 131
2.2.4. Orientability 137
§2.3. The structure of the Seiberg Witten invariants 139
2.3.1. The universal line bundle 139
2.3.2. The case b% 1 142
2.3.3. The case 6^ = 1 154
2.3.4. Some examples 169
§2.4. Applications 176
2.4.1. The Seiberg Witten equations on cylinders 176
2.4.2. The Thorn conjecture 183
2.4.3. Negative definite smooth 4 manifolds 188
Chapter 3. Seiberg Witten Equations on Complex Surfaces 195
§3.1. A short trip in complex geometry 195
3.1.1. Basic notions 195
3.1.2. Examples of complex surfaces 213
3.1.3. Kodaira classification of complex surfaces 225
§3.2. Seiberg Witten invariants of Kahler surfaces 228
3.2.1. Seiberg Witten equations on Kahler surfaces 228
3.2.2. Monopoles, vortices and divisors 233
3.2.3. Deformation theory 242
§3.3. Applications 245
3.3.1. A nonvanishing result 246
3.3.2. Seiberg Witten invariants of simply connected elliptic
surfaces 252
3.3.3. The failure of the /i cobordism theorem in four
dimensions 274
3.3.4. Seiberg Witten equations on symplectic 4 manifolds 275
Chapter 4. Gluing Techniques 283
§4.1. Elliptic equations on manifolds with cylindrical ends 283
4.1.1. Manifolds with cylindrical ends 283
4.1.2. The Atiyah Patodi Singer index theorem 286
4.1.3. Eta invariants and spectral flows 292
4.1.4. The Lockhart McOwen theory 298
4.1.5. Abstract linear gluing results 303
4.1.6. Examples 309
§4.2. Finite energy monopoles 328
4.2.1. Regularity 328
4.2.2. Three dimensional monopoles 330
4.2.3. Asymptotic behavior. Part I 338
4.2.4. Asymptotic behavior. Part II 344
4.2.5. Proofs of some technical results 359
§4.3. Moduli spaces of finite energy monopoles: Local aspects 368
4.3.1. Functional set up 368
4.3.2. The Kuranishi picture 383
4.3.3. Virtual dimensions 397
4.3.4. Reducible finite energy monopoles 404
§4.4. Moduli spaces of finite energy monopoles: Global aspects 409
4.4.1. Genericity results 409
4.4.2. Compactness properties 412
4.4.3. Orientability issues 425
§4.5. Cutting and pasting of monopoles 428
4.5.1. Some basic gluing constructions 429
4.5.2. Gluing monopoles: Local theory 435
4.5.3. The local surjectivity of the gluing construction 447
4.5.4. Gluing monopoles: Global theory 451
§4.6. Applications 460
4.6.1. Vanishing results 461
4.6.2. Blow up formula 465
Epilogue 471
Bibliography 473
Index 481
|
| any_adam_object | 1 |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2 |
| dewey-search | 514/.2 |
| dewey-sort | 3514 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013518563 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:47:12Z |
| institution | BVB |
| isbn | 9780821821459 0821821458 |
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| physical | XVIII, 484 S. graph. Darst. |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Nicolaescu, Liviu I. 1964- Verfasser (DE-588)124402887 aut Notes on Seiberg-Witten theory Liviu I. Nicolaescu Providence, RI American Math. Soc. 2000 XVIII, 484 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 28 Analyse globale (Mathématiques) Physique mathématique Seiberg-Witten, Invariants de Variétés topologiques à 4 dimensions Mathematische Physik Four-manifolds (Topology) Global analysis (Mathematics) Mathematical physics Seiberg-Witten invariants Seiberg-Witten-Invariante (DE-588)4430370-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Seiberg-Witten-Invariante (DE-588)4430370-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2083-3 Graduate studies in mathematics 28 (DE-604)BV009739289 28 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009227056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nicolaescu, Liviu I. 1964- Notes on Seiberg-Witten theory Graduate studies in mathematics Analyse globale (Mathématiques) Physique mathématique Seiberg-Witten, Invariants de Variétés topologiques à 4 dimensions Mathematische Physik Four-manifolds (Topology) Global analysis (Mathematics) Mathematical physics Seiberg-Witten invariants Seiberg-Witten-Invariante (DE-588)4430370-1 gnd |
| subject_GND | (DE-588)4430370-1 (DE-588)4113937-9 |
| title | Notes on Seiberg-Witten theory |
| title_auth | Notes on Seiberg-Witten theory |
| title_exact_search | Notes on Seiberg-Witten theory |
| title_full | Notes on Seiberg-Witten theory Liviu I. Nicolaescu |
| title_fullStr | Notes on Seiberg-Witten theory Liviu I. Nicolaescu |
| title_full_unstemmed | Notes on Seiberg-Witten theory Liviu I. Nicolaescu |
| title_short | Notes on Seiberg-Witten theory |
| title_sort | notes on seiberg witten theory |
| topic | Analyse globale (Mathématiques) Physique mathématique Seiberg-Witten, Invariants de Variétés topologiques à 4 dimensions Mathematische Physik Four-manifolds (Topology) Global analysis (Mathematics) Mathematical physics Seiberg-Witten invariants Seiberg-Witten-Invariante (DE-588)4430370-1 gnd |
| topic_facet | Analyse globale (Mathématiques) Physique mathématique Seiberg-Witten, Invariants de Variétés topologiques à 4 dimensions Mathematische Physik Four-manifolds (Topology) Global analysis (Mathematics) Mathematical physics Seiberg-Witten invariants Seiberg-Witten-Invariante Hochschulschrift |
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