Heat Kernels and Dirac Operators

Berline, Nicole

ISBN 10: 0387533400 / ISBN 13: 9780387533407

Published by Secaucus, New Jersey, U.S.A.: Springer Verlag, 1992

About this Item

**International edition** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service.

Seller Inventory # ABE-8191677992

Bibliographic Details

• Title: Heat Kernels and Dirac Operators
• Publisher: Secaucus, New Jersey, U.S.A.: Springer Verlag
• Publication Date: 1992
• Language: English
• ISBN 10: 0387533400
• ISBN 13: 9780387533407
• Binding: Soft cover
• Edition: 1st Edition
• Condition: New
• Dust Jacket Condition: New

About this title

Synopsis

In this book, the Atiyah-Singer index theorem for Dirac operators on compact Riemannian manifolds and its more recent generalizations receive simple proofs. The main technique which is used is an explicit geometric construction of the heat kernels of a generalized Dirac operator. The first four chapters could be used at 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. Several chapters deal with other preparatory material.

From the Back Cover

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.