Heat Kernels and Dirac Operators

Nicole Berline, Ezra Getzler, Michèle Vergne

363 pages, parution le 17/12/2003

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Résumé

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.

Written for:
Graduate students and researchers in differential geometry, Arakelov geometry, group representation theory and mathematical physics

Introduction
Background on Differential Geometry
Asymptotic Expansion of the Heat Kernel
Clifford Modules and Dirac Operators
Index Density of Dirac Operators
The Exponential Map and the Index Density
The Equivariant Index Theorem
Equivariant Differential Forms
The Kirillov Formula for the Equivariant Index
The Index Bundle
The Family Index Theorem

References
List of Notation
Index

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Nicole Berline, Ezra Getzler, Michèle Vergne
Parution	17/12/2003
Nb. de pages	363
Format	15,5 x 23,5
Couverture	Broché
Poids	576g
Intérieur	Noir et Blanc
EAN13	9783540200628