Gauge theory and the topology of four-manifolds:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Providence, RI
American Math. Soc., Inst. for Advanced Study
1998
|
| Series: | Park City Mathematics Institute: IAS / Park City Mathematics Series
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 221 S. |
| ISBN: | 0821805916 |
Staff View
MARC
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| 245 | 1 | 0 | |a Gauge theory and the topology of four-manifolds |c Robert Friedman ..., ed. |
| 264 | 1 | |a Providence, RI |b American Math. Soc., Inst. for Advanced Study |c 1998 | |
| 300 | |a X, 221 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Park City Mathematics Institute: IAS / Park City Mathematics Series |v 4 | |
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Record in the Search Index
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| adam_text |
Contents
Preface ix
Introduction 1
David Gieseker, Geometric Invariant Theory and the Moduli of
Bundles 5
Lecture 1. Geometric Invariant Theory 7
Lecture 2. The Numerical Criterion 11
Lecture 3. The Moduli of Stable Bundles 13
References 21
Jun Li, Anti Self Dual Connections and Stable Vector Bundles 23
Introduction 25
Lecture 1. Hermitian Bundles, Hermitian Connections and Their Curvatures 27
Lecture 2. Hermitian Einstein Connections and Stable Vector Bundles 33
Lecture 3. The Existence of Hermitian Einstein Metrics 41
References 49
John W. Morgan, An Introduction to Gauge Theory 51
Lecture 1. The Context of Gauge Theory 53
1.1. Problems 55
Lecture 2. Principal Bundles and Connections 59
2.1. Principal bundles 59
2.2. Examples of principal bundles 60
2.3. The transition functions 61
2.4. Pullback bundles 62
2.5. Associated bundles 62
2.6. Universal bundles 63
2.7. Connections on smooth principal bundles 65
2.8. The differential form description of a connection 65
V
vi CONTENTS
2.9. Existence of connections 66
2.10. Covariant differentiation 67
2.11. Problems 68
Lecture 3. Curvature and Characteristic Classes 71
3.1. The curvature of a connection as an obstruction to integrating the
horizontal distribution 71
3.2. Interpretation of the curvature in terms of the connection one form 73
3.3. The relationship of curvature and covariant differentiation 74
3.4. Characteristic classes 75
3.5. The holonomy of a connection 76
3.6. Problems 77
Lecture 4. The Space of Connections 81
4.1. The group of bundle isomorphisms of P 81
4.2. Infinite dimensional manifolds, a first version 82
4.3. The action of the group of gauge of transformations on the space of
connections 83
4.4. The space of gauge equivalence classes of connections 85
4.5. The local structure of the quotient space 90
4.6. Problems 90
Lecture 5. The ASD Equations and the Moduli Space 95
5.1. The ASD equations and the moduli space 95
5.2. The local structure of the moduli space 96
5.3. The generic metrics theorem 99
5.4. Reducible connections 100
5.5. Orientability of M*(P) 101
5.6. Variation of the metric 102
5.7. Problems 103
Lecture 6. Compactness and Gluing Theorems 109
6.1. Uhlenbeck compactness 109
6.2. Gluing together connections 112
6.3. Taubes' gluing theorem 113
6.4. The moduli space of instantons over S4 115
6.5. The ends of M{P) 116
6.6. Negative definite 4 manifolds 117
6.7. Problems 120
Lecture 7. The Donaldson Polynomial Invariants 123
7.1. The formalism of the Donaldson polynomial invariants 123
7.2. The ^ map 124
7.3. The Uhlenbeck compactification of the moduli space 126
7.4. Extension of the /x map over the compactification 127
7.5. Definition of the Donaldson polynomial invariants in the stable range 128
7.6. A blow up formula and the unstable range 129
7.7. The Donaldson series 130
7.8. Problems 131
Lecture 8. The Connected Sum Theorem 135
CONTENTS vii
8.1. The main results 135
8.2. The divisors in B£(Q) representing fi(x) 136
8.3. The Taubes gluing setup of the connected sum theorem 137
8.4. The sketch of the argument for the connected sum theorem 139
8.5. The non vanishing theorem 140
8.6. Problems 141
References 143
Ronald J. Stern, Computing Donaldson Invariants 145
Abstract 147
Lecture 1. Overview 149
1.1. Classical invariants 149
1.2. Existence 151
1.3. Uniqueness (The Donaldson Invariant) 153
Lecture 2. —2 Spheres and the Blowup Formula 161
2.1. Ruberman's theorem 161
2.2. The recursion scheme 164
2.3. Universal relations 166
2.4. The ODE 167
2.5. Solving the ODE 168
2.6. The simple type condition 169
Lecture 3. Simple Type Criteria and Elliptic Surfaces 173
3.1. Manifolds with big diffeomorphism group 173
3.2. A simple type criteria 175
3.3. The Donaldson series for the K3 surface 176
3.4. Another simple type criteria 176
3.5. The Donaldson series for elliptic surfaces 176
Lecture 4. Elementary Rational Blowdowns 179
4.1. Elementary rational blowdowns 179
4.2. Logarithmic transform as rational blowdown 180
4.3. The basic computational theorem 181
4.4. The Donaldson series for E(n;p,q) 182
Lecture 5. Taut Configurations and Horikowa Surfaces 187
5.1. Taut configurations 187
5.2. Horikowa surfaces 188
References 191
Clifford H. Taubes and James A. Bryan, Donaldson Floer Theory 195
Abstract 197
Lecture 1. Introduction 199
1.1. Motivation 199
1.2. The moduli space and the invariants 200
1.3. A strategy to compute the invariants 202
viii CONTENTS
Lecture 2. Quantization 205
2.1. Problems 205
2.2. Quantization and the Chern Simons functional 207
Lecture 3. Simplicial Decomposition of M°x 211
3.1. The decomposition 211
3.2. Formal consequences 213
3.3. Problems revisited 214
Lecture 4. Half Infinite Dimensional Spaces 217
References 221 |
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| genre | (DE-588)1071861417 Konferenzschrift 1994 Park City Utah gnd-content |
| genre_facet | Konferenzschrift 1994 Park City Utah |
| id | DE-604.BV011804293 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T05:20:08Z |
| institution | BVB |
| isbn | 0821805916 |
| language | English |
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| physical | X, 221 S. |
| publishDate | 1998 |
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| publisher | American Math. Soc., Inst. for Advanced Study |
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| series2 | Park City Mathematics Institute: IAS / Park City Mathematics Series |
| spelling | Gauge theory and the topology of four-manifolds Robert Friedman ..., ed. Providence, RI American Math. Soc., Inst. for Advanced Study 1998 X, 221 S. txt rdacontent n rdamedia nc rdacarrier Park City Mathematics Institute: IAS / Park City Mathematics Series 4 Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dimension 4 (DE-588)4338676-3 gnd rswk-swf Eichtheorie (DE-588)4122125-4 gnd rswk-swf Gittereichtheorie (DE-588)4157377-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1994 Park City Utah gnd-content Gittereichtheorie (DE-588)4157377-8 s Topologische Mannigfaltigkeit (DE-588)4185712-4 s DE-604 Eichtheorie (DE-588)4122125-4 s Mannigfaltigkeit (DE-588)4037379-4 s Dimension 4 (DE-588)4338676-3 s Friedman, Robert 1955- Sonstige (DE-588)120046180 oth Erscheint auch als Online-Ausgabe 978-1-4704-3903-3 Park City Mathematics Series Park City Mathematics Institute: IAS 4 (DE-604)BV010402400 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007969766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gauge theory and the topology of four-manifolds Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 4 (DE-588)4338676-3 gnd Eichtheorie (DE-588)4122125-4 gnd Gittereichtheorie (DE-588)4157377-8 gnd |
| subject_GND | (DE-588)4185712-4 (DE-588)4037379-4 (DE-588)4338676-3 (DE-588)4122125-4 (DE-588)4157377-8 (DE-588)1071861417 |
| title | Gauge theory and the topology of four-manifolds |
| title_auth | Gauge theory and the topology of four-manifolds |
| title_exact_search | Gauge theory and the topology of four-manifolds |
| title_full | Gauge theory and the topology of four-manifolds Robert Friedman ..., ed. |
| title_fullStr | Gauge theory and the topology of four-manifolds Robert Friedman ..., ed. |
| title_full_unstemmed | Gauge theory and the topology of four-manifolds Robert Friedman ..., ed. |
| title_short | Gauge theory and the topology of four-manifolds |
| title_sort | gauge theory and the topology of four manifolds |
| topic | Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 4 (DE-588)4338676-3 gnd Eichtheorie (DE-588)4122125-4 gnd Gittereichtheorie (DE-588)4157377-8 gnd |
| topic_facet | Topologische Mannigfaltigkeit Mannigfaltigkeit Dimension 4 Eichtheorie Gittereichtheorie Konferenzschrift 1994 Park City Utah |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007969766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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