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Global Analysis on Foliated Spaces

  • Calvin C. Moore
  • Claude Schochet

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 9)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Calvin C. Moore, Claude Schochet
    Pages 1-15
  3. Calvin C. Moore, Claude Schochet
    Pages 16-37
  4. Calvin C. Moore, Claude Schochet
    Pages 38-67
  5. Calvin C. Moore, Claude Schochet
    Pages 68-91
  6. Calvin C. Moore, Claude Schochet
    Pages 92-136
  7. Calvin C. Moore, Claude Schochet
    Pages 137-162
  8. Calvin C. Moore, Claude Schochet
    Pages 163-206
  9. Calvin C. Moore, Claude Schochet
    Pages 207-259
  10. Calvin C. Moore, Claude Schochet
    Pages 260-278
  11. Back Matter
    Pages 279-337

About this book

Introduction

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.

Keywords

Characteristic class cohomology geometry homology operator algebra

Authors and affiliations

  • Calvin C. Moore
    • 1
    • 2
  • Claude Schochet
    • 3
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Mathematical Sciences Research InstituteBerkeleyUSA
  3. 3.Department of MathematicsWayne State UniversityDetroitUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9592-8
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9594-2
  • Online ISBN 978-1-4613-9592-8
  • Series Print ISSN 0940-4740
  • Buy this book on publisher's site