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OverviewGlobal analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem [ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families [AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory. Full Product DetailsAuthor: Calvin C. Moore , Claude SchochetPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 1988 Volume: 9 Dimensions: Width: 15.50cm , Height: 1.80cm , Length: 23.50cm Weight: 0.528kg ISBN: 9781461395942ISBN 10: 1461395941 Pages: 337 Publication Date: 14 December 2011 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsI. Locally Traceable Operators.- II. Foliated Spaces.- III. Tangential Cohomology.- IV. Transverse Measures.- V. Characteristic Classes.- VI. Operator Algebras.- VII. Pseudodifferential Operators.- VIII. The Index Theorem.- Appendices.- C: Positive Scalar Curvature Along the Leaves.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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