John Roe

Elliptic Operators, Topology, and Asymptotic Methods (eBook, ePUB)

• Format: ePub

Produktbeschreibung

Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important exampl

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Erscheinungstermin: 19. Dezember 2013
• Englisch
• ISBN-13: 9781040211885
• Artikelnr.: 73256763

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