| Introduction |
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xiii | |
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1 | (102) |
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Bundles, connections and characteristic classes |
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1 | (15) |
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Vector bundles and connections |
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1 | (11) |
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12 | (4) |
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Basic facts about elliptic equations |
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16 | (11) |
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Clifford algebras and Dirac operators |
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27 | (26) |
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Clifford algebras and their representations |
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27 | (7) |
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The Spin and Spinc groups |
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34 | (6) |
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Spin and spinc structures |
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40 | (6) |
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Dirac operators associated to spin and spinc structures |
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46 | (7) |
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Complex differential geometry |
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53 | (32) |
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Elementary complex differential geometry |
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54 | (14) |
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68 | (12) |
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Dirac operators on almost Kahler manifolds |
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80 | (5) |
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85 | (18) |
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Continuous families of elliptic operators |
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85 | (15) |
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100 | (3) |
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The Seiberg-Witten Invariants |
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103 | (92) |
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103 | (11) |
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The Seiberg-Witten equations |
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103 | (5) |
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108 | (6) |
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The structure of the Seiberg-Witten moduli spaces |
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114 | (25) |
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The topology of the moduli spaces |
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114 | (5) |
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The local structure of the moduli spaces |
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119 | (12) |
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131 | (6) |
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137 | (2) |
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The structure of the Seiberg-Witten invariants |
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139 | (37) |
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The universal line bundle |
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139 | (3) |
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142 | (12) |
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154 | (15) |
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169 | (7) |
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176 | (19) |
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The Seiberg-Witten equations on cylinders |
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176 | (7) |
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183 | (5) |
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Negative definite smooth 4-manifolds |
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188 | (7) |
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Seiberg-Witten Equations on Complex Surfaces |
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195 | (88) |
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A short trip in complex geometry |
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195 | (33) |
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195 | (18) |
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Examples of complex surfaces |
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213 | (12) |
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Kodaira classification of complex surfaces |
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225 | (3) |
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Seiberg-Witten invariants of Kahler surfaces |
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228 | (17) |
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Seiberg-Witten equations on Kahler surfaces |
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228 | (5) |
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Monopoles, vortices and divisors |
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233 | (9) |
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242 | (3) |
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245 | (38) |
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246 | (6) |
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Seiberg-Witten invariants of simply connected elliptic surfaces |
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252 | (22) |
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The failure of the h-cobordism theorem in four dimensions |
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274 | (1) |
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Seiberg-Witten equations on symplectic 4-manifolds |
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275 | (8) |
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283 | (188) |
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Elliptic equations on manifolds with cylindrical ends |
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283 | (45) |
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Manifolds with cylindrical ends |
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283 | (3) |
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The Atiyah-Patodi-Singer index theorem |
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286 | (6) |
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Eta invariants and spectral flows |
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292 | (6) |
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The Lockhart-McOwen theory |
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298 | (5) |
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Abstract linear gluing results |
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303 | (6) |
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309 | (19) |
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328 | (40) |
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328 | (2) |
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Three-dimensional monopoles |
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330 | (8) |
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Asymptotic behavior. Part I |
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338 | (6) |
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Asymptotic behavior. Part II |
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344 | (15) |
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Proofs of some technical results |
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359 | (9) |
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Moduli spaces of finite energy monopoles: Local aspects |
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368 | (41) |
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368 | (15) |
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383 | (14) |
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397 | (7) |
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Reducible finite energy monopoles |
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404 | (5) |
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Moduli spaces of finite energy monopoles: Global aspects |
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409 | (19) |
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409 | (3) |
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412 | (13) |
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425 | (3) |
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Cutting and pasting of monopoles |
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428 | (32) |
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Some basic gluing constructions |
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429 | (6) |
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Gluing monopoles: Local theory |
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435 | (12) |
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The local surjectivity of the gluing construction |
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447 | (4) |
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Gluing monopoles: Global theory |
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451 | (9) |
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460 | (11) |
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461 | (4) |
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465 | (6) |
| Epilogue |
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471 | (2) |
| Bibliography |
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473 | (8) |
| Index |
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481 | |
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