The Index Theorem and the Heat Equation Method (Nankai Tracts in Mathematics) by Yanlin Yu (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “The book is self-contained, which is most helpful for graduate students.” — Mathematical Reviews, 2002The book is self-contained, which is most helpful for graduate students. — Mathematical Reviews, 2002it is reasonably self-contained and could serve as the starting point for studies of the index theorem. — Mathematics Abstracts, 2002

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