Heat kernels and Dirac operators
著者
書誌事項
Heat kernels and Dirac operators
（Die Grundlehren der mathematischen Wissenschaften, 298）
Springer, c1996
- : gw
- : us
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注記
"Second corrected printing 1996"--T.p. verso
Includes bibliographical references (p. [355]-359) and index
内容説明・目次
内容説明
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent generalizations, are presented. The formula for the index of the Dirac operator is obtained from the classical formula for the heat kernel of the harmonic oscillator. The only prerequisite to reading this book is a familiarity with basic differential geometry. There are several chapters of preparatory material, including a treatment of connections and Quillen's theory of superconnections, characteristic classes, the theory of the heat equation and its solution on a compact manifold, Clifford algebras, Dirac operators and equivariant differential forms. The book finishes with a treatment of the index bundle and Bismut's local version of the Atiyah-Singer Index Theorem for families. As an application, the curvature of the determinant line bundle is calculated, following Bismut and Freed.
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