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Heat Kernels and Dirac Operators : Grundlehren Text Editions - Nicole Berline

Heat Kernels and Dirac Operators

Grundlehren Text Editions

Paperback

Published: 8th December 2003
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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.

Aus den Rezensionen: "! Das vorliegende Buch ist die zweite korrigierte und erweiterte Ausgabe eines Werkes aus dem Jahre 1992. ! Ausgehend von einer Grundausbildung in klassischer Differentialgeometrie stellt das Buch alle zum Verstandnis des Beweises notwendigen Voraussetzungen zur Verfugung. Dadurch eignet es sich einerseits zum Selbststudium fur Studierende mit entsprechender Vorbildung ! andererseits als Grundlage einer Vorlesung uber dieses ergiebige Thema." (P. Grabner, in: IMN - Internationale Mathematische Nachrichten, 2006, Issue 202, S. 45)

Introductionp. 1
Background on Differential Geometryp. 13
Asymptotic Expansion of the Heat Kernelp. 61
Clifford Modules and Dirac Operatorsp. 99
Index Density of Dirac Operatorsp. 139
The Exponential Map and the Index Densityp. 163
The Equivariant Index Theoremp. 181
Equivariant Differential Formsp. 203
The Kirillov Formula for the Equivariant Indexp. 243
The Index Bundlep. 263
The Family Index Theoremp. 311
Referencesp. 349
List of Notationp. 355
Indexp. 359
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540200628
ISBN-10: 3540200622
Series: Grundlehren Text Editions
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 363
Published: 8th December 2003
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.4 x 14.7  x 2.3
Weight (kg): 0.57