Mathematical Sciences Research Institute Publications

Global Analysis on Foliated Spaces

Authors: Moore, Calvin C., Schochet, Claude

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About this book

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.

Buy this book

eBook n/a
  • ISBN 978-1-4613-9592-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-1-4613-9594-2
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Bibliographic Information

Bibliographic Information
Book Title
Global Analysis on Foliated Spaces
Authors
Series Title
Mathematical Sciences Research Institute Publications
Series Volume
9
Copyright
1988
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4613-9592-8
DOI
10.1007/978-1-4613-9592-8
Softcover ISBN
978-1-4613-9594-2
Series ISSN
0940-4740
Edition Number
1
Number of Pages
VII, 337
Topics