Index Theorem And The Heat Equation Method, The

ISBN: 9789810246105 出版年：2001 页码：309 Yanlin Yu Weiping Zhang World Scientific Publishing Company

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.