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Mathematics - Geometry & Topology | Heat Kernels and Dirac Operators

Heat Kernels and Dirac Operators

Berline, Nicole, Getzler, Ezra, Vergne, Michèle

Originally published as Volume 298 in the series: "Grundlehren der mathematischen Wissenschaften", 1992

1992, IX, 363 p.

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  • About this textbook

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.

Content Level » Research

Keywords » 53C05 - 58A10 - 58G10 - 58G11 - Atiyah-Singer Index Theorem - Dirac Operators - Heat Kernel Differential Geometry - Superconnections - YellowSale2006

Related subjects » Algebra - Geometry & Topology - Theoretical, Mathematical & Computational Physics

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