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Spin geometry /
This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas requ...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
1989.
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| Colección: | Princeton mathematical series ;
38. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Dedication; Contents; PREFACE ; ACKNOWLEDGMENTS ; INTRODUCTION ; CHAPTER I Clifford Algebras, Spin Groups and Their Representations ; 1. Clifford algebras ; 2. The groups Pin and Spin ; 3. The algebras Cln and Clr, s; 4. The classification ; 5. Representations ; 6. Lie algebra structures.
- 7. Some direct applications to geometry 8. Some further applications to the theory of Lie groups ; 9. K-theory and the Atiyah-Bott-Shapiro construction ; 10. KR-theory and the (1,1)-Periodicity Theorem ; CHAPTER II Spin Geometry and the Dirac Operators.
- 1. Spin structures on vector bundles 2. Spin manifolds and spin cobordism ; 3. Clifford and spinor bundles ; 4. Connections on spinor bundles ; 5. The Dirac operators ; 6. The fundamental elliptic operators ; 7. Clk-linear Dirac operators; 8. Vanishing theorems and some applications.
- CHAPTER III Index Theorems 1. Differential operators ; 2. Sobolev spaces and Sobolev theorems ; 3. Pseudodifferential operators ; 4. Elliptic operators and parametrices ; 5. Fundamental results for elliptic operators ; 6. The heat kernel and the index.
- 7. The topological invariance of the index 8. The index of a family of elliptic operators ; 9. The G-index ; 10. The Clifford index ; 11. Multiplicative sequences and the Chern character ; 12. Thorn isomorphisms and the Chern character defect.