Index Theorem And The Heat Equation Method, The

Yanlin Yu (Autor)

Buch | Hardcover

308 Seiten

2001
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-4610-5 (ISBN)

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This volume provides a self-contained represenation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first-order geometric elliptic operators by using the heat-equation method.

This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods.

Preliminaries in Riemannian geometry; Schroedinger and heat operators; MP parametrix and applications; Chern-Weil theory; Clifford algebra and super-algebra; Dirac operator; local index theorems; Riemann-Roch theorem.

Erscheint lt. Verlag	4.7.2001
Reihe/Serie	Nankai Tracts in Mathematics ; 2
Mitarbeit	Herausgeber (Serie): Weiping Zhang
Verlagsort	Singapore
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	981-02-4610-2 / 9810246102
ISBN-13	978-981-02-4610-5 / 9789810246105
Zustand	Neuware