The Resource The SeibergWitten equations and applications to the topology of smooth fourmanifolds, John W. Morgan
The SeibergWitten equations and applications to the topology of smooth fourmanifolds, John W. Morgan
 Summary
 The recent introduction of the SeibergWitten invariants of smooth fourmanifolds has revolutionized the study of those manifolds. The invariants are gaugetheoretic in nature and are close cousins of the muchstudied 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 SeibergWitten 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 SeibergWitten 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 SeibergWitten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)case, the SeibergWitten moduli spaces are shown to be compact. The SeibergWitten invariant is then essentially the homology class in the space of configurations represented by the SeibergWitten 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
 Language
 eng
 Extent
 1 online resource (137 pages).
 Contents

 7. Invariants of Kahler Surfaces
 Bibliography
 Frontmatter
 Contents
 1. Introduction
 2. Clifford Algebras and Spin Groups
 3. Spin Bundles and the Dirac Operator
 4. The SeibergWitten Moduli Space
 5. Curvature Identities and Bounds
 6. The SeibergWitten Invariant
 Isbn
 9781400865161
 Label
 The SeibergWitten equations and applications to the topology of smooth fourmanifolds
 Title
 The SeibergWitten equations and applications to the topology of smooth fourmanifolds
 Statement of responsibility
 John W. Morgan
 Language
 eng
 Summary
 The recent introduction of the SeibergWitten invariants of smooth fourmanifolds has revolutionized the study of those manifolds. The invariants are gaugetheoretic in nature and are close cousins of the muchstudied 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 SeibergWitten 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 SeibergWitten 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 SeibergWitten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)case, the SeibergWitten moduli spaces are shown to be compact. The SeibergWitten invariant is then essentially the homology class in the space of configurations represented by the SeibergWitten 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
 Cataloging source
 E7B
 Index
 no index present
 Language note
 In English
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Mathematical Notes
 Series volume
 44
 Label
 The SeibergWitten equations and applications to the topology of smooth fourmanifolds, John W. Morgan
 Bibliography note
 Includes bibliographical references
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents

 7. Invariants of Kahler Surfaces
 Bibliography
 Frontmatter
 Contents
 1. Introduction
 2. Clifford Algebras and Spin Groups
 3. Spin Bundles and the Dirac Operator
 4. The SeibergWitten Moduli Space
 5. Curvature Identities and Bounds
 6. The SeibergWitten Invariant
 http://library.link/vocab/cover_art
 https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9781400865161&userID=ebscotest&password=ebscotest
 Dimensions
 unknown
 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b4332605'}
 Extent
 1 online resource (137 pages).
 Form of item
 online
 Isbn
 9781400865161
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Specific material designation
 remote
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.rpi.edu/portal/TheSeibergWittenequationsandapplicationsto/2SRwnjZ1Bgg/" typeof="WorkExample http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.rpi.edu/portal/TheSeibergWittenequationsandapplicationsto/2SRwnjZ1Bgg/">The SeibergWitten equations and applications to the topology of smooth fourmanifolds, John W. Morgan</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.lib.rpi.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.rpi.edu/">Rensselaer Libraries</a></span></span></span></span></div>