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Volume 14, Number 2 , Review: Peter B. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem. Dodziuk : Review: Peter B. Atiyah Oxford , R. Bott Cambridge, Mass. Patodi Bombay The joint paper of the above title which appeared in Inventiones math.
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. 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 Bismuts Local Family Index Theorem for Dirac operators. The early modern town in Scotland London, ,
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