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catalog contributor b11849788.
catalog created "2000.".
catalog date "2000".
catalog date "2000.".
catalog dateCopyrighted "2000.".
catalog description "103 -- 2.1.1. The Seiberg-Witten equations 103 -- 2.1.2. The functional set-up 108 -- 2.2. The structure of the Seiberg-Witten moduli spaces 114 -- 2.2.1. The topology of the moduli spaces 114 -- 2.2.2. The local structure of the moduli spaces 119 -- 2.2.3. Generic smoothness 131 -- 2.2.4. Orientability 137 -- 2.3. The structure of the Seiberg-Witten invariants 139 -- 2.3.1. The universal line bundle 139 -- 2.3.2. The case b[superscript + subscript 2]> 1 142 -- 2.3.3. The case b[superscript + subscript 2] = 1 154 -- 2.3.4. Some examples 169 -- 2.4. Applications 176 -- 2.4.1. The Seiberg-Witten equations on cylinders 176 -- 2.4.2. The Thom conjecture 183 -- 2.4.3. Negative definite smooth 4-manifolds 188 -- Chapter 3. Seiberg-Witten Equations on Complex Surfaces 195 -- 3.1. A short trip in complex geometry 195 -- 3.1.1. Basic notions 195 -- 3.1.2.".
catalog description "303 -- 4.2. Finite energy monopoles 328 -- 4.2.1. Regularity 328 -- 4.2.2. Three-dimensional monopoles 330 -- 4.2.3. Asymptotic behavior 338 -- 4.2.5. Proofs of some technical results 359 -- 4.3. Moduli spaces of finite energy monopoles: Local aspects 368 -- 4.3.1. Functional set-up 368 -- 4.3.2. The Kuranishi picture 383 -- 4.3.3. Virtual dimensions 397 -- 4.3.4. Reducible finite energy monopoles 404 -- 4.4. Moduli spaces of finite energy monopoles: Global aspects 409 -- 4.4.1. Genericity results 409 -- 4.4.2. Compactness properties 412 -- 4.4.3. Orientability issues 425 -- 4.5. Cutting and pasting of monopoles 428 -- 4.5.1. Some basic gluing constructions 429 -- 4.5.2. Gluing monopoles: Local theory 435 -- 4.5.3. The local surjectivity of the gluing construction 447 -- 4.5.4. Gluing monopoles: Global theory 451 -- 4.6. Applications 460 -- 4.6.1.".
catalog description "Chapter 1. Preliminaries 1 -- 1.1. Bundles, connections and characteristic classes 1 -- 1.1.1. Vector bundles and connections 1 -- 1.1.2. Chern-Weil theory 12 -- 1.2. Basic facts about elliptic equations 16 -- 1.3. Clifford algebras and Dirac operators 27 -- 1.3.1. Clifford algebras and their representations 27 -- 1.3.2. The Spin and Spin[superscript c] groups 34 -- 1.3.3. Spin and spin[superscript c] structures 40 -- 1.3.4. Dirac operators associated to spin and spin[superscript c] structures 46 -- 1.4. Complex differential geometry 53 -- 1.4.1. Elementary complex differential geometry 54 -- 1.4.2. Cauchy-Riemann operators 68 -- 1.4.3. Dirac operators on almost Kahler manifolds 80 -- 1.5. Fredholm theory 85 -- 1.5.1. Continuous families of elliptic operators 85 -- 1.5.2. Genericity results 100 -- Chapter 2. The Seiberg-Witten Invariants 103 -- 2.1. Seiberg-Witten monopoles".
catalog description "Examples of complex surfaces 213 -- 3.1.3. Kodaira classification of complex surfaces 225 -- 3.2. Seiberg-Witten invariants of Kahler surfaces 228 -- 3.2.1. Seiberg-Witten equations on Kahler surfaces 228 -- 3.2.2. Monopoles, vortices and divisors 233 -- 3.2.3. Deformation theory 242 -- 3.3. Applications 245 -- 3.3.1. A nonvanishing result 246 -- 3.3.2. Seiberg-Witten invariants of simply connected elliptic surfaces 252 -- 3.3.3. The failure of the h-cobordism theorem in four dimensions 274 -- 3.3.4. Seiberg-Witten equations on symplectic 4-manifolds 275 -- Chapter 4. Gluing Techniques 283 -- 4.1. Elliptic equations on manifolds with cylindrical ends 283 -- 4.1.1. Manifolds with cylindrical ends 283 -- 4.1.2. The Atiyah-Patodi-Singer index theorem 286 -- 4.1.3. Eta invariants and spectral flows 292 -- 4.1.4. The Lockhart-McOwen theory 298 -- 4.1.5. Abstract linear gluing results".
catalog description "Includes bibliographical references and index.".
catalog description "Vanishing results 461 -- 4.6.2. Blow-up formula 465.".
catalog extent "xviii, 484 p. :".
catalog identifier "0821821458".
catalog isPartOf "Graduate studies in mathematics ; v. 28".
catalog issued "2000".
catalog issued "2000.".
catalog language "eng".
catalog publisher "Providence, RI : American Mathematical Society,".
catalog subject "514/.2 21".
catalog subject "Four-manifolds (Topology)".
catalog subject "Global analysis (Mathematics)".
catalog subject "Mathematical physics.".
catalog subject "QA614 .N53 2000".
catalog subject "Seiberg-Witten invariants.".
catalog tableOfContents "103 -- 2.1.1. The Seiberg-Witten equations 103 -- 2.1.2. The functional set-up 108 -- 2.2. The structure of the Seiberg-Witten moduli spaces 114 -- 2.2.1. The topology of the moduli spaces 114 -- 2.2.2. The local structure of the moduli spaces 119 -- 2.2.3. Generic smoothness 131 -- 2.2.4. Orientability 137 -- 2.3. The structure of the Seiberg-Witten invariants 139 -- 2.3.1. The universal line bundle 139 -- 2.3.2. The case b[superscript + subscript 2]> 1 142 -- 2.3.3. The case b[superscript + subscript 2] = 1 154 -- 2.3.4. Some examples 169 -- 2.4. Applications 176 -- 2.4.1. The Seiberg-Witten equations on cylinders 176 -- 2.4.2. The Thom conjecture 183 -- 2.4.3. Negative definite smooth 4-manifolds 188 -- Chapter 3. Seiberg-Witten Equations on Complex Surfaces 195 -- 3.1. A short trip in complex geometry 195 -- 3.1.1. Basic notions 195 -- 3.1.2.".
catalog tableOfContents "303 -- 4.2. Finite energy monopoles 328 -- 4.2.1. Regularity 328 -- 4.2.2. Three-dimensional monopoles 330 -- 4.2.3. Asymptotic behavior 338 -- 4.2.5. Proofs of some technical results 359 -- 4.3. Moduli spaces of finite energy monopoles: Local aspects 368 -- 4.3.1. Functional set-up 368 -- 4.3.2. The Kuranishi picture 383 -- 4.3.3. Virtual dimensions 397 -- 4.3.4. Reducible finite energy monopoles 404 -- 4.4. Moduli spaces of finite energy monopoles: Global aspects 409 -- 4.4.1. Genericity results 409 -- 4.4.2. Compactness properties 412 -- 4.4.3. Orientability issues 425 -- 4.5. Cutting and pasting of monopoles 428 -- 4.5.1. Some basic gluing constructions 429 -- 4.5.2. Gluing monopoles: Local theory 435 -- 4.5.3. The local surjectivity of the gluing construction 447 -- 4.5.4. Gluing monopoles: Global theory 451 -- 4.6. Applications 460 -- 4.6.1.".
catalog tableOfContents "Chapter 1. Preliminaries 1 -- 1.1. Bundles, connections and characteristic classes 1 -- 1.1.1. Vector bundles and connections 1 -- 1.1.2. Chern-Weil theory 12 -- 1.2. Basic facts about elliptic equations 16 -- 1.3. Clifford algebras and Dirac operators 27 -- 1.3.1. Clifford algebras and their representations 27 -- 1.3.2. The Spin and Spin[superscript c] groups 34 -- 1.3.3. Spin and spin[superscript c] structures 40 -- 1.3.4. Dirac operators associated to spin and spin[superscript c] structures 46 -- 1.4. Complex differential geometry 53 -- 1.4.1. Elementary complex differential geometry 54 -- 1.4.2. Cauchy-Riemann operators 68 -- 1.4.3. Dirac operators on almost Kahler manifolds 80 -- 1.5. Fredholm theory 85 -- 1.5.1. Continuous families of elliptic operators 85 -- 1.5.2. Genericity results 100 -- Chapter 2. The Seiberg-Witten Invariants 103 -- 2.1. Seiberg-Witten monopoles".
catalog tableOfContents "Examples of complex surfaces 213 -- 3.1.3. Kodaira classification of complex surfaces 225 -- 3.2. Seiberg-Witten invariants of Kahler surfaces 228 -- 3.2.1. Seiberg-Witten equations on Kahler surfaces 228 -- 3.2.2. Monopoles, vortices and divisors 233 -- 3.2.3. Deformation theory 242 -- 3.3. Applications 245 -- 3.3.1. A nonvanishing result 246 -- 3.3.2. Seiberg-Witten invariants of simply connected elliptic surfaces 252 -- 3.3.3. The failure of the h-cobordism theorem in four dimensions 274 -- 3.3.4. Seiberg-Witten equations on symplectic 4-manifolds 275 -- Chapter 4. Gluing Techniques 283 -- 4.1. Elliptic equations on manifolds with cylindrical ends 283 -- 4.1.1. Manifolds with cylindrical ends 283 -- 4.1.2. The Atiyah-Patodi-Singer index theorem 286 -- 4.1.3. Eta invariants and spectral flows 292 -- 4.1.4. The Lockhart-McOwen theory 298 -- 4.1.5. Abstract linear gluing results".
catalog tableOfContents "Vanishing results 461 -- 4.6.2. Blow-up formula 465.".
catalog title "Notes on Seiberg-Witten theory / Liviu I. Nicolaescu.".
catalog type "text".