4-manifolds and Kirby calculus:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Soc.
1999
|
| Schriftenreihe: | Graduate studies in mathematics
20 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 558 S. graph. Darst. |
| ISBN: | 0821809946 9780821809945 |
Internformat
MARC
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| 245 | 1 | 0 | |a 4-manifolds and Kirby calculus |c Robert E. Gompf ; András I. Stipscz |
| 246 | 1 | 3 | |a Four-manifolds and kirby calculus |
| 264 | 1 | |a Providence, RI |b American Mathematical Soc. |c 1999 | |
| 300 | |a XV, 558 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804128029904994304 |
|---|---|
| adam_text | Contents
Preface xi
Part 1. 4 Manifolds 1
Chapter 1. Introduction 3
§1.1. Manifolds 3
§1.2. 4 manifolds 7
§1.3. Examples 18
§1.4. Appendix 24
Chapter 2. Surfaces in 4 manifolds 37
§2.1. Surfaces in CP2 37
§2.2. The blow up process 41
§2.3. Desingularization of curves 47
§2.4. Appendix: Introduction to gauge theory 51
Chapter 3. Complex surfaces 67
§3.1. E(l) and fiber sum 67
§3.2. Other constructions of elliptic fibrations 77
§3.3. Logarithmic transformation 82
§3.4. Classification of complex surfaces 85
Part 2. Kirby Calculus 97
Chapter 4. Handlebodies and Kirby diagrams 99
§4.1. Handles 99
vii
viii Contents
§4.2. Handle decompositions 104
§4.3. Dimension three — Heegaard splittings 112
§4.4. Dimension four — Kirby diagrams 115
§4.5. Linking numbers and framings 120
§4.6. Examples 126
Chapter 5. Kirby calculus 139
§5.1. Handle moves 139
§5.2. Surgery 153
§5.3. Dehn surgery 157
§5.4. 1 handles revisited 167
§5.5. Relative Kirby calculus 175
§5.6. Spin structures 180
§5.7. Spin structures in Kirby diagrams 184
Chapter 6. More examples 197
§6.1. Plumbings and related constructions 197
§6.2. Embedded surfaces and their complements 207
§6.3. Branched covers 225
Part 3. Applications 237
Chapter 7. Branched covers and resolutions 239
§7.1. Definitions and examples 239
§7.2. Resolution of singularities 246
§7.3. Elliptic surfaces revisited 256
§7.4. Surfaces of general type 270
Chapter 8. Elliptic and Lefschetz fibrations 283
§8.1. Lefschetz pencils and fibrations 284
§8.2. The topology of Lefschetz fibrations 292
§8.3. The topology of elliptic surfaces 303
§8.4. Higher genus and generalized fibrations 320
§8.5. Rationally blowing down 330
Chapter 9. Cobordisms, /i cobordisms and exotic R4 s 339
§9.1. Cobordism groups 340
§9.2. fa cobordisms 346
§9.3. Akbulut corks and exotic M4 s 357
Contents ix
§9.4. More exotica 366
Chapter 10. Symplectic 4 manifolds 385
§10.1. Symplectic and almost complex manifolds 385
§10.2. Constructions of symplectic manifolds 393
§10.3. 4 manifolds with no symplectic structure 406
§10.4. Gauge theory on symplectic 4 manifolds 412
Chapter 11. Stein surfaces 419
§11.1. Contact structures 419
§11.2. Kir by diagrams of Stein surfaces 427
§11.3. Invariants of Stein and contact structures 436
§11.4. Stein surfaces and gauge theory 446
Part 4. Appendices 453
Chapter 12. Solutions 455
§12.1. Solutions of some exercises in Part 1 455
§12.2. Solutions of some exercises in Part 2 460
§12.3. Solutions of some exercises in Part 3 501
Chapter 13. Notation, important figures 533
§13.1. List of commonly used notation 533
§13.2. Index of important diagrams 536
§13.3. Index of Kirby moves and related operations 539
Bibliography 541
Index 553
|
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| dewey-ones | 514 - Topology |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013264664 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:42:45Z |
| institution | BVB |
| isbn | 0821809946 9780821809945 |
| language | English |
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| spelling | Gompf, Robert E. 1957- Verfasser (DE-588)17333542X aut 4-manifolds and Kirby calculus Robert E. Gompf ; András I. Stipscz Four-manifolds and kirby calculus Providence, RI American Mathematical Soc. 1999 XV, 558 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 20 Dimension 4 (DE-588)4338676-3 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Henkelkörper (DE-588)4511570-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Henkelkörper (DE-588)4511570-9 s Topologie (DE-588)4060425-1 s DE-604 Mannigfaltigkeit (DE-588)4037379-4 s Dimension 4 (DE-588)4338676-3 s Stipsicz, András 1966- Verfasser (DE-588)138530785 aut Erscheint auch als Online-Ausgabe 978-1-4704-1797-0 Graduate studies in mathematics 20 (DE-604)BV009739289 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009042673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gompf, Robert E. 1957- Stipsicz, András 1966- 4-manifolds and Kirby calculus Graduate studies in mathematics Dimension 4 (DE-588)4338676-3 gnd Topologie (DE-588)4060425-1 gnd Henkelkörper (DE-588)4511570-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4338676-3 (DE-588)4060425-1 (DE-588)4511570-9 (DE-588)4037379-4 (DE-588)4113937-9 |
| title | 4-manifolds and Kirby calculus |
| title_alt | Four-manifolds and kirby calculus |
| title_auth | 4-manifolds and Kirby calculus |
| title_exact_search | 4-manifolds and Kirby calculus |
| title_full | 4-manifolds and Kirby calculus Robert E. Gompf ; András I. Stipscz |
| title_fullStr | 4-manifolds and Kirby calculus Robert E. Gompf ; András I. Stipscz |
| title_full_unstemmed | 4-manifolds and Kirby calculus Robert E. Gompf ; András I. Stipscz |
| title_short | 4-manifolds and Kirby calculus |
| title_sort | 4 manifolds and kirby calculus |
| topic | Dimension 4 (DE-588)4338676-3 gnd Topologie (DE-588)4060425-1 gnd Henkelkörper (DE-588)4511570-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | Dimension 4 Topologie Henkelkörper Mannigfaltigkeit Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009042673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
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