دانلود کتاب Spin Geometry (PMS-38), Volume 38

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Contents\nPreface\nAcknowledgments\nIntroduction\nChapter I. Clifford Algebras, Spin Groups and Their Representations\n §1. Clifford algebras\n §2. The groups Pin and Spin\n §3. The algebras Cln and Clrs\n §4. The classification\n §5. Representations\n §6. Lie algebra structures\n §7. Some direct applications to geometry\n §8. Some further applications to the theory of Lie groups\n §9. K-theory and the Atiyah-Bott-Shapiro construction\n §10. KR-theory and the (1,1\r)-Periodicity Theorem\nChapter II. Spin Geometry and the Dirac Operators\n §1. Spin structures on vector bundles\n §2. Spin manifolds and spin cobordism\n §3. Clifford and spinor bundles\n §4. Connections on spinor bundles\n §5. The Dirac operators\n §6. The fundamental elliptic operators\n §7. Clk\r-linear Dirac operators\n §8. Vanishing theorems and some applications\nChapter III. Index Theorems\n §1. Differential operators\n §2. Sobolev spaces and Sobolev theorems\n §3. Pseudodifferential operators\n §4. Elliptic operators and parametrices\n §5. Fundamental results for elliptic operators\n §6. The heat kernel and the index\n §7. The topological invariance of the index\n §8. The index ofafamily of elliptic operators\n §9. The G-index\n §10. The Clifford index\n §11. Multiplicative sequences and the Chern character\n §12. Thom isomorphisms and the Chern character defect\n §13. The Atiyah-Singer Index Theorem\n §14. Fixed-point formulas for elliptic operators\n §15. The Index Theorem for Families\n §16. Families of real operators and the Clk-in\rdex Theorem\n §17. Remarks on heat and supersymmetry\nChapter IV. Applications in Geometry and Topology\n §1. Integrality theorems\n §2. Immersions of manifolds and the vector field problem\n §3. Group actions on manifolds\n §4. Compact manifolds of positive scalar curvature\n §5. Positive scalar curvature and the fundamental group\n §6. Complete manifolds of positive scalar curvature\n §7. The topology of the space of positive scalar curvature metrics\n §8. Clifford multiplication and Kähler\r manifolds\n §9. Pure spinors, complex structures, and twistors\n §10. Reduced holonomy and calibrations\n §11. Spinor cohomology and complex manifolds with vanishing first Chern class\n §12. The Positive Mass Conjecture in general relativity\nAppendix A. Principal G-bundles\nAppendix B. Classifying Spaces and Characteristic Classes\nAppendix C. Orientation Classes and Thom Isomorphisms in K-theory\nAppendix D. Spinc-manifolds\nBibliography\nIndex\nNotation Index