Heat Kernels and Dirac Operators 1992 Edition Contributor(s): Berline, Nicole (Author), Getzler, Ezra (Author), Vergne, Michèle (Author) |
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ISBN: 3540200622 ISBN-13: 9783540200628 Publisher: Springer OUR PRICE: $66.49 Product Type: Paperback Published: December 2003 Annotation: 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. |
Additional Information |
BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Group Theory - Science | Physics - Mathematical & Computational |
Dewey: 515.353 |
LCCN: 2003070710 |
Series: Grundlehren Text Editions |
Physical Information: 0.78" H x 6.14" W x 9.21" (1.17 lbs) 363 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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. |