《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
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這是我見過的處理局部指標定理最棒的一本書~此書言簡意賅，幾乎每一段話都有它的用意！沒讀一遍，總有收獲！推薦給有誌於深入學習指標定理的人！
评分自鏇幾何的升級版：重新詮釋狄拉剋算子是量子化的聯絡理論，狄拉剋算子的平方根的熱核的超跡是聯絡對應的陳特徵。依照這個詮釋，狄拉剋的指標理論是熱核與陳特徵的關係，而這個關係不僅僅是上同調類的而是微分形式的，則指標理論和熱核作為量子化的陳韋伊理論。熱核算子是投影算子和恒等算子的插值。重新詮釋和尋找新的聯係
评分自鏇幾何的升級版：重新詮釋狄拉剋算子是量子化的聯絡理論，狄拉剋算子的平方根的熱核的超跡是聯絡對應的陳特徵。依照這個詮釋，狄拉剋的指標理論是熱核與陳特徵的關係，而這個關係不僅僅是上同調類的而是微分形式的，則指標理論和熱核作為量子化的陳韋伊理論。熱核算子是投影算子和恒等算子的插值。重新詮釋和尋找新的聯係
评分自鏇幾何的升級版：重新詮釋狄拉剋算子是量子化的聯絡理論，狄拉剋算子的平方根的熱核的超跡是聯絡對應的陳特徵。依照這個詮釋，狄拉剋的指標理論是熱核與陳特徵的關係，而這個關係不僅僅是上同調類的而是微分形式的，則指標理論和熱核作為量子化的陳韋伊理論。熱核算子是投影算子和恒等算子的插值。重新詮釋和尋找新的聯係
评分自鏇幾何的升級版：重新詮釋狄拉剋算子是量子化的聯絡理論，狄拉剋算子的平方根的熱核的超跡是聯絡對應的陳特徵。依照這個詮釋，狄拉剋的指標理論是熱核與陳特徵的關係，而這個關係不僅僅是上同調類的而是微分形式的，則指標理論和熱核作為量子化的陳韋伊理論。熱核算子是投影算子和恒等算子的插值。重新詮釋和尋找新的聯係
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