John Roe

Elliptic Operators, Topology, and Asymptotic Methods

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Pitman Research Notes In Mathematics Series
• Verlag: Pearson Education Limited
• 2 ed
• Seitenzahl: 218
• Erscheinungstermin: 6. Januar 1999
• Englisch
• Abmessung: 245mm x 170mm x 11mm
• Gewicht: 346g
• ISBN-13: 9780582325029
• ISBN-10: 0582325021
• Artikelnr.: 22947510

Autorenporträt

John Roe

Inhaltsangabe

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