商品描述
The first edition of this book presented simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut), using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive softcover. The first four chapters could be used as the text for a graduate course on the applications of linear elliptic operators in differential geometry and the only prerequisites are a familiarity with basic differential geometry. The next four chapters discuss the equivariant index theorem, and include a useful introduction to equivariant differential forms. The last two chapters give a proof, in the spirit of the book, of Bismut's Local Family Index Theorem for Dirac operators.
商品描述(中文翻譯)
本書的第一版提供了關於緊緻黎曼流形上Dirac算子的Atiyah-Singer指數定理及其推廣（由作者及J.-M. Bismut提出）的簡單證明，並使用了廣義Dirac算子的熱核的明確幾何構造；新版本以吸引人的平裝本形式，使這本受歡迎的書籍能夠提供給學生和研究人員。前四章可以作為研究生課程的教材，主題為線性橢圓算子在微分幾何中的應用，唯一的先決條件是對基本微分幾何的熟悉。接下來的四章討論了等變指數定理，並包括對等變微分形式的有用介紹。最後兩章則以本書的精神提供了Bismut的局部族指數定理對於Dirac算子的證明。
