Heat Kernels and Dirac Operators (Grundlehren der mathematischen Wissenschaften) - Hardcover

Berline, Nicole; Getzler, Ezra; Vergne, Michèle

Hardcover

ISBN 10: 3540533400 ISBN 13: 9783540533405

Verlag: Springer, 2003

Inhaltsangabe

In the first edition of this book, 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) were presented, 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 paperback.

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In the first edition of this book, 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) were presented, 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 paperback. 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. This book will be of interest to graduate students and researchers in differential geometry, Arakelov geometry, group representation theory and mathematical physics.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2003
• Sprache: Englisch
• ISBN 10: 3540533400
• ISBN 13: 9783540533405
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 363
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar