The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[1995]
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| Schriftenreihe: | Mathematical Notes
44 |
| Schlagworte: | |
| Online-Zugang: | UBM01 Volltext |
| Beschreibung: | The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces |
| Beschreibung: | 1 Online-Ressource (130p.) |
| ISBN: | 9781400865161 |
| DOI: | 10.1515/9781400865161 |
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| 500 | |a The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Morgan, John W. |
| author_facet | Morgan, John W. |
| author_role | aut |
| author_sort | Morgan, John W. |
| author_variant | j w m jw jwm |
| building | Verbundindex |
| bvnumber | BV042524173 |
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| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400865161 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:24:04Z |
| institution | BVB |
| isbn | 9781400865161 |
| language | English |
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| publishDate | 1995 |
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| spelling | Morgan, John W. Verfasser aut The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds John W. Morgan Princeton, N.J. Princeton University Press [1995] 1 Online-Ressource (130p.) txt rdacontent c rdamedia cr rdacarrier Mathematical Notes 44 The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces In English Mathematik Four-manifolds (Topology) Seiberg-Witten invariants Mathematical physics MATHEMATICS / Topology bisacsh Mathematische Physik Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Seiberg-Witten-Invariante (DE-588)4430370-1 gnd rswk-swf Dimension 4 (DE-588)4338676-3 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s Dimension 4 (DE-588)4338676-3 s Seiberg-Witten-Invariante (DE-588)4430370-1 s 1\p DE-604 Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s Mathematische Physik (DE-588)4037952-8 s 2\p DE-604 https://doi.org/10.1515/9781400865161 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Morgan, John W. The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds Mathematik Four-manifolds (Topology) Seiberg-Witten invariants Mathematical physics MATHEMATICS / Topology bisacsh Mathematische Physik Mathematische Physik (DE-588)4037952-8 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Seiberg-Witten-Invariante (DE-588)4430370-1 gnd Dimension 4 (DE-588)4338676-3 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4185712-4 (DE-588)4012269-4 (DE-588)4430370-1 (DE-588)4338676-3 |
| title | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds |
| title_auth | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds |
| title_exact_search | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds |
| title_full | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds John W. Morgan |
| title_fullStr | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds John W. Morgan |
| title_full_unstemmed | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds John W. Morgan |
| title_short | The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds |
| title_sort | the seiberg witten equations and applications to the topology of smooth four manifolds |
| topic | Mathematik Four-manifolds (Topology) Seiberg-Witten invariants Mathematical physics MATHEMATICS / Topology bisacsh Mathematische Physik Mathematische Physik (DE-588)4037952-8 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Seiberg-Witten-Invariante (DE-588)4430370-1 gnd Dimension 4 (DE-588)4338676-3 gnd |
| topic_facet | Mathematik Four-manifolds (Topology) Seiberg-Witten invariants Mathematical physics MATHEMATICS / Topology Mathematische Physik Topologische Mannigfaltigkeit Differenzierbare Mannigfaltigkeit Seiberg-Witten-Invariante Dimension 4 |
| url | https://doi.org/10.1515/9781400865161 |
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