Heat Kernels and Dirac Operators (Grundlehren Text Editions)

Berline, Nicole/ Getzler, Ezra/ Vergne, Michele

Springer（2004/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 362 p.
• 商品コード 9783540200628

基本説明

New in softcover. Hardcover is out of print. 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. Originally published as Volume 298 in the series: "Grundlehren der mathematischen Wissenschaften", 1992.

Full Description

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.