Heat Kernels and Dirac Operators
Synopsis
The first edition of this book presented simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut), using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive softcover. The first four chapters could be used as the text for a graduate course on the applications of linear elliptic operators in differential geometry and the only prerequisites are a familiarity with basic differential geometry. The next four chapters discuss the equivariant index theorem, and include a useful introduction to equivariant differential forms. The last two chapters give a proof, in the spirit of the book, of Bismut's Local Family Index Theorem for Dirac operators.Book details
- Edition:
- 1st ed. 2004
- Series:
- Grundlehren Text Editions
- Author:
- Nicole Berline, Ezra Getzler, Michèle Vergne
- ISBN:
- 9783642580888
- Related ISBNs:
- 9783540200628
- Publisher:
- Springer Berlin Heidelberg
- Pages:
- N/A
- Reading age:
- Not specified
- Includes images:
- No
- Date of addition:
- 2024-05-10
- Usage restrictions:
- Copyright
- Copyright date:
- 2004
- Copyright by:
- N/A
- Adult content:
- No
- Language:
- English
- Categories:
- Earth Sciences, Mathematics and Statistics, Nonfiction