TY - BOOK UR - http://lib.ugent.be/catalog/ebk01:3710000000222320 ID - ebk01:3710000000222320 LA - eng TI - The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds PY - 1995 SN - 9781400865161 AU - Morgan, John W., author. AB - 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. ER -Download RIS file
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001 | 9781400865161 | ||
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008 | 150324s1995||||||||||||o|||||||||||eng|| | ||
020 | a 9781400865161 | ||
024 | 7 | a 10.1515/9781400865161 2 doi | |
035 | a (DE-B1597)447694 | ||
035 | a (OCoLC)891400523 | ||
040 | a IN-ChSCO b eng c IN-ChSCO e rda | ||
041 | a eng | ||
050 | 4 | a QA613.2 | |
050 | 1 | 4 | a QA613.2 b .M67 1996eb |
072 | 7 | a MAT x 038000 2 bisacsh | |
072 | 7 | a MAT038000 2 bisacsh | |
082 | 4 | a 514/.2 2 20 | |
082 | 4 | a 514/.2 2 23 | |
100 | 1 | a Morgan, John W., e author. | |
245 | 1 | 4 | a The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds / c John W. Morgan. |
264 | 1 | a Princeton, N.J. : b Princeton University Press, c [1995] | |
264 | 4 | c Â©1995 | |
300 | a 1 online resource(130p.) : b illustrations. | ||
336 | a text 2 rdacontent | ||
337 | a computer 2 rdamedia | ||
338 | a online resource 2 rdacarrier | ||
347 | a text file b PDF 2 rda | ||
490 | a Mathematical Notes ; v 44 | ||
505 | t Frontmatter -- t Contents -- t 1. Introduction -- t 2. Clifford Algebras and Spin Groups -- t 3. Spin Bundles and the Dirac Operator -- t 4. The Seiberg-Witten Moduli Space -- t 5. Curvature Identities and Bounds -- t 6. The Seiberg-Witten Invariant -- t 7. Invariants of Kahler Surfaces -- t Bibliography. | ||
520 | 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. | ||
533 | a Electronic reproduction. b Princeton, N.J. : c Princeton University Press, d 1995. n Mode of access: World Wide Web. n System requirements: Web browser. n Access may be restricted to users at subscribing institutions. | ||
538 | a Mode of access: Internet via World Wide Web. | ||
545 | a MorganJohn W.: John W. Morgan is Professor of Mathematics at Columbia University. | ||
546 | a In English. | ||
588 | a Description based on online resource; title from PDF title page (publisherâ€™s Web site, viewed March 24, 2015) | ||
650 | a Four-manifolds (Topology) | ||
650 | a Mathematical physics. | ||
650 | a Seiberg-Witten invariants. | ||
650 | 4 | a Four-manifolds (Topology). | |
650 | 4 | a Geometry and Topology. | |
650 | 4 | a Mathematical physics. | |
650 | 4 | a Mathematics. | |
650 | 4 | a Seiberg-Witten invariants. | |
650 | 7 | a MATHEMATICS x Topology. 2 bisacsh. | |
650 | 7 | a Mathematik. | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Archive 1931-1999 z 978-3-11-044249-6 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Mathematical Notes Backlist eBook Package z 978-3-11-049492-1 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Univ. Press eBook Package 2014 z 978-3-11-041342-7 | |
856 | 4 | u https://doi.org/10.1515/9781400865161 | |
856 | 4 | 2 | 3 Cover u https://www.degruyter.com/doc/cover/9781400865161.jpg |
912 | a 978-3-11-041342-7 Princeton Univ. Press eBook Package 2014 | ||
912 | a 978-3-11-044249-6 Princeton eBook Package Archive 1931-1999 | ||
912 | a 978-3-11-049492-1 Princeton Mathematical Notes Backlist eBook Package | ||
912 | a GBV-deGruyter-alles | ||
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912 | a GBV-deGruyter-PDA1ALL | ||
912 | a GBV-deGruyter-PDA3STM | ||
912 | a GBV-deGruyter-PDA5EBK | ||
912 | a GBV-deGruyter-PDA7ENG | ||
912 | a GBV-deGruyter-PDA9PRIN |
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