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.

Heat Kernels and Dirac Operators (Grundlehren Text Editions)

Science & Math

Berline, Nicole

Mathematics

Springer, Verlag

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.

Heat Kernels and Dirac Operators (Grundlehren der mathematischen Wissenschaften)

Vergne, Michèle

Getzler, Ezra

Springer

This book is a comprehensive presentation of entity-relationship (ER) modeling with regard to an integrated development and modeling of database applications. It comprehensively surveys the achievements of research in this field and deals with the ER model and its extensions. In addition, the book presents techniques for the translation of the ER model into classical database models and languages, such as relational, hierarchical, and network models and languages, as well as into object-oriented models.

Business & Money

Management & Leadership

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Books by Berline, Nicole