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Global Analysis on Foliated Spaces
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Catalogue Information
Field name
Details
Dewey Class
514.2
Title
Global Analysis on Foliated Spaces ([EBook]) / by Calvin C. Moore, Claude Schochet.
Author
Moore, Calvin C. , 1936-
Added Personal Name
Schochet, Claude
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : Springer , 1988.
Physical Details
VII, 337 pages : online resource.
Series
Mathematical Sciences Research Institute publications
0940-4740 ; ; 9
ISBN
9781461395928
Summary Note
Global 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.:
Contents note
I. 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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4613-9592-8
Links to Related Works
Subject References:
Algebraic Topology
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Foliations (Mathematics)
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Global analysis (Mathematics)
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Mathematics
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Theoretical, Mathematical and Computational Physics
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Authors:
author
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Moore, Calvin C. 1936-
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Schochet, Claude
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SpringerLink (Online service)
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Series:
Mathematical Sciences Research Institute publications
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Classification:
514.2
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