Grundlehren Text Editions

Berline, Nicole; Getzler, Ezra; Vergne, Michèle

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.

Details

Published by: Springer

Publication Date: 2003-12-08

Format: Paperback

ISBN-13: 9783540200628

DOI: 10.1007/978-3-642-58088-8

Dimensions: 235cm x155cm

Pages: 363