Elliptic Operators, Topology, and Asymptotic Methods

List of contents

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

Summary

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.

Product details

• Authors: John Roe, John (Penn State University Roe, Roe John
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Hardback
• Released: 31.12.2017
• EAN: 9781138417670
• ISBN: 978-1-138-41767-0
• No. of pages: 218
• Series: Chapman & Hall/CRC Research Notes in Mathematics Series
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; MATHEMATICS / Differential Equations / General, Differential calculus & equations, Differential calculus and equations