Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Grundlehren Text Editions (TEXTEDITIONS)
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About this book
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.
Keywords
Table of contents (11 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Heat Kernels and Dirac Operators
Authors: Nicole Berline, Ezra Getzler, Michèle Vergne
Series Title: Grundlehren Text Editions
DOI: https://doi.org/10.1007/978-3-642-58088-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2004
Hardcover ISBN: 978-3-540-53340-5Due: 16 December 1991
Softcover ISBN: 978-3-540-20062-8Published: 08 December 2003
eBook ISBN: 978-3-642-58088-8Published: 09 May 2024
Series ISSN: 1618-2685
Series E-ISSN: 2627-5260
Edition Number: 1
Number of Pages: IX, 363
Additional Information: Originally published as Volume 298 in the series: "Grundlehren der mathematischen Wissenschaften", 1992
Topics: Differential Geometry, Group Theory and Generalizations, Theoretical, Mathematical and Computational Physics, Mathematical Methods in Physics, Numerical and Computational Physics, Simulation