Heat Kernels and Dirac Operators
Michele Vergne author Ezra Getzler author Nicole Berline author
Format:Paperback
Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Published:8th Dec '03
Currently unavailable, and unfortunately no date known when it will be back
Springer Book Archives
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.
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)
ISBN: 9783540200628
Dimensions: unknown
Weight: unknown
363 pages