The index theorem is a central result of modern mathematics and all students of global analysis need to be familiar with it. This edition preserves the brevity of the first edition, but includes new material and reworkings of some of the more difficult arguments.
The index theorem is a central result of modern mathematics and all students of global analysis need to be familiar with it. This edition preserves the brevity of the first edition, but includes new material and reworkings of some of the more difficult arguments.
Chapter 1. Resume of Riemannian geometry Chapter 2. Connections curvature and characteristic classes Chapter 3. Clifford algebras and Dirac operators Chapter 4. The Spin groups Chapter 5. Analytic properties of Dirac operators Chapter 6. Hodge theory Chapter 7. The heat and wave equations Chapter 8. Traces and eigenvalue asymptotics Chapter 9. Some non-compact manifolds Chapter 10. The Lefschetz formula Chapter 11. The index problem Chapter 12. The Getzler calculus and the local index theorem Chapter 13. Applications of the index theorem Chapter 14. Witten's approach to Morse theory Chapter 15. Atiyah's T-index theorem References
Chapter 1. Resume of Riemannian geometry Chapter 2. Connections curvature and characteristic classes Chapter 3. Clifford algebras and Dirac operators Chapter 4. The Spin groups Chapter 5. Analytic properties of Dirac operators Chapter 6. Hodge theory Chapter 7. The heat and wave equations Chapter 8. Traces and eigenvalue asymptotics Chapter 9. Some non-compact manifolds Chapter 10. The Lefschetz formula Chapter 11. The index problem Chapter 12. The Getzler calculus and the local index theorem Chapter 13. Applications of the index theorem Chapter 14. Witten's approach to Morse theory Chapter 15. Atiyah's T-index theorem References
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