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The Seiberg-Witten equations and applications to the topology of smooth four-manifolds:

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Bibliographic Details
Main Author:	Morgan, John W. 1946- (Author)
Format:	Book
Language:	English
Published:	Princeton, NJ Princeton Univ. Press 1996
Series:	Mathematical notes 44
Subjects:	Dimension 4 Seiberg-Witten-Invariante Topologische Mannigfaltigkeit Mathematische Physik Differenzierbare Mannigfaltigkeit
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007154830&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	VI, 128 S.
ISBN:	0691025975

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adam_text	THE SEIBERG-WITTEN EQUATIONS AND APPLICATIONS TO THE TOPOLOGY OF SMOOTH FOUR-MANIFOLDS BY JOHN W. MORGAN MATHEMATICAL NOTES 44 PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY 1996 CONTENTS 1 INTRODUCTION 1 2 CLIFFORD ALGEBRAS AND SPIN GROUPS 5 2.1 THE CLIFFORD ALGEBRAS 5 2.2 THE GROUPS PIN(V) AND SPIN(V) 9 2.3 SPLITTING OF THE CLIFFORD ALGEBRA 13 2.4 THE COMPLEXIFICATION OF THE CL{V) 16 2.5 THE COMPLEX SPIN REPRESENTATION 19 2.6 THE GROUP SPIN C (V) 20 3 SPIN BUNDLES AND THE DIRAC OPERATOR 23 3.1 SPIN BUNDLES AND CLIFFORD BUNDLES 23 3.2 CONNECTIONS AND CURVATURE 28 3.3 THE DIRAC OPERATOR 40 3.4 THE CASE OF COMPLEX MANIFOLDS 48 4 THE SEIBERG-WITTEN MODULI SPACE 55 4.1 THE EQUATIONS 55 4.2 SPACE OF CONFIGURATIONS 57 4.3 GROUP OF CHANGES OF GAUGE 59 4.4 THE ACTION 59 4.5 THE QUOTIENT SPACE 60 4.6 THE ELLIPTIC COMPLEX 65 5 CURVATURE IDENTITIES AND BOUNDS 69 5.1 CURVATURE IDENTITIES 70 5.2 A PRIORI BOUNDS 77 5.3 THE COMPACTNESS OF THE MODULI SPACE 80 VI CONTENTS 6 THE SEIBERG-WITTEN INVARIANT 87 6.1 THE STATEMENT 87 6.2 THE PARAMETRIZED MODULI SPACE 88 6.3 REDUCIBLE SOLUTIONS 91 6.4 COMPACTNESS OF THE PERTURBED MODULI SPACE 92 6.5 VARIATION OF THE METRIC AND SELF-DUAL TWO-FORM 94 6.6 ORIENTABILITY OF THE MODULI SPACE 95 6.7 THE CASE WHEN B$(X) 1 99 6.8 AN INVOLUTION IN THE THEORY 100 6.9 THE CASE WHEN B${X) = 1 104 7 INVARIANTS OF KAHLER SURFACES 109 7.1 THE EQUATIONS OVER A KAHLER MANIFOLD 109 7.2 HOLOMORPHIC DESCRIPTION OF THE MODULI SPACE 112 7.3 EVALUATION FOR KAHLER SURFACES 118 7.4 COMPUTATION FOR KAHLER SURFACES 122 7.5 FINAL REMARKS 126 BIBLIOGRAPHY 127
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spellingShingle	Morgan, John W. 1946- The Seiberg-Witten equations and applications to the topology of smooth four-manifolds Mathematical notes Dimension 4 (DE-588)4338676-3 gnd Seiberg-Witten-Invariante (DE-588)4430370-1 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Mathematische Physik (DE-588)4037952-8 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd
subject_GND	(DE-588)4338676-3 (DE-588)4430370-1 (DE-588)4185712-4 (DE-588)4037952-8 (DE-588)4012269-4
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 by John W. Morgan
title_fullStr	The Seiberg-Witten equations and applications to the topology of smooth four-manifolds by John W. Morgan
title_full_unstemmed	The Seiberg-Witten equations and applications to the topology of smooth four-manifolds by 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	Dimension 4 (DE-588)4338676-3 gnd Seiberg-Witten-Invariante (DE-588)4430370-1 gnd Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Mathematische Physik (DE-588)4037952-8 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd
topic_facet	Dimension 4 Seiberg-Witten-Invariante Topologische Mannigfaltigkeit Mathematische Physik Differenzierbare Mannigfaltigkeit
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007154830&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000003793
work_keys_str_mv	AT morganjohnw theseibergwittenequationsandapplicationstothetopologyofsmoothfourmanifolds

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