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Elliptic Operators, Topology, and Asymptotic Methods
ISBN-13:
9781482247831
Veröffentl:
2013
Seiten:
209
Autor:
John Roe
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
0 - No protection
Sprache:
Englisch
Beschreibung:
The index theorem continues to stand as a central result of modern mathematics. In a concise presentation that offers streamlined analyses and coverage of important examples and applications, this book introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. It assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, this becomes the ideal vehicle for self-study or coursework. Anyone working with index theory or supersymmetry will find it a succinct but wide-ranging introduction to this important and intriguing field.
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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