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Heat Kernels and Dirac Operators

Librairie Eyrolles - Paris 5e
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Heat Kernels and Dirac Operators

Heat Kernels and Dirac Operators

363 pages, parution le 17/12/2003

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

Contents

  • 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

L'auteur Nicole Berline

Autres livres de Nicole Berline

Caractéristiques techniques du livre "Heat Kernels and Dirac Operators"

  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

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