《熱核與狄拉剋算子(英文版)》講述瞭：This book, which began as a seminar in 1985 at MIT, contains complete proofs of thelocal index theorem for Dirac operators using the heat kernel approach, together withits generalizations to equivariant Dirac operators and families of Dirac operators, aswell as background material on superconnections and equivariant differential forms.

Since the publication of the first edition, the subjects treated here have contin-ued to find new applications. Equivariant cohomology plays an important role in thestudy of symplectic reduction, and Bismut superconnections and the local index the-orem for families have had many applications, through the construction of higheranalytic torsion forms and currents. （For a survey of some of these developments,we recommend reading Bismut's talk at the Berlin International Congress of Mathe-maticians, reference

Although this book lacks some of the usual attributes of a textbook （such asexercises）, it has been widely used in advanced courses in differential geometry;for many of the topics discussed here, there are no other treatments available inmonograph form. Because of the continuing demand from students for the book,we were very