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Book 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

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Heat Kernels and Dirac Operators
• Author: Nicole Berline
• Language: English
• Binding: Paperback
• Number of pages: 363
• EAN: 9783540200628
• ISBN: 3540200622
• ID: 04446423
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 582 g
• Dimensions: 156 × 233 × 24 mm
• Date of publishing: 08. December 2003

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