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OverviewThis Research Note gives an introduction to the circle of ideas surrounding the `heat equation proof' of the Atiyah-Singer index theorem. Asymptotic expansions for the solutions of partial differential equations on compact manifolds are used to obtain topological information, by means of a `supersymmetric' cancellation of eigenspaces. The analysis is worked out in the context of Dirac operators on Clifford bundles. The work includes proofs of the Hodge theorem; eigenvalue estimates; the Lefschetz theorem; the index theorem; and the Morse inequalities. Examples illustrate the general theory, and several recent results are included. This new edition has been revised to streamline some of the analysis and to give better coverage of important examples and applications. Readership: The book is aimed at researchers and graduate students with a background in differential geometry and functional analysis. Full Product DetailsAuthor: John RoePublisher: Pearson Education Limited Imprint: Longman Edition: 2nd edition Volume: Vol. 395 Dimensions: Width: 24.40cm , Height: 1.10cm , Length: 16.90cm Weight: 0.335kg ISBN: 9780582325029ISBN 10: 0582325021 Pages: 216 Publication Date: 18 August 1998 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: No Longer Our Product Availability: Out of print, replaced by POD  We will order this item for you from a manufatured on demand supplier. Table of ContentsIntroduction Chapter 1 Resumé of Riemannian geometry Chapter 2 Connections, curvature, and characteristic class Chapter 3 Clifford algebras and Dirac operators Chapter 4 The Spin groups Chapter 5 Analytic properties of Dirac operators Chapter 6 Hodge theory Chapter 7 The heat and wave equations Chapter 8 Traces and eigenvalue asymptotics Chapter 9 Some non-compact manifolds Chapter 10 The Lefschetz formula Chapter 11 The index problem Chapter 12 The Getzler calculus and the local index theorem Chapter 13 Applications of the index theorem Chapter 14 Witten's approach to Morse theory Chapter 15 Atiyah's GAMMA-index theorem ReferencesReviewsAuthor InformationJohn Roe Tab Content 6Author Website:Countries AvailableAll regions |
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