Global Analysis on Foliated Spaces

1. Front Matter

   Pages i-vii

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2. Introduction

   • Calvin C. Moore, Claude Schochet

   Pages 1-15

3. Locally Traceable Operators

   • Calvin C. Moore, Claude Schochet

   Pages 16-37

4. Foliated Spaces

   • Calvin C. Moore, Claude Schochet

   Pages 38-67

5. Tangential Cohomology

   • Calvin C. Moore, Claude Schochet

   Pages 68-91

6. Transverse Measures

   • Calvin C. Moore, Claude Schochet

   Pages 92-136

7. Characteristic Classes

   • Calvin C. Moore, Claude Schochet

   Pages 137-162

8. Operator Algebras

   • Calvin C. Moore, Claude Schochet

   Pages 163-206

9. Pseudodifferential Operators

   • Calvin C. Moore, Claude Schochet

   Pages 207-259

10. The Index Theorem

    • Calvin C. Moore, Claude Schochet

    Pages 260-278

11. Back Matter

    Pages 279-337

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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.

• Characteristic class
• cohomology
• geometry
• homology
• operator algebra

• Department of Mathematics, University of California, Berkeley, USA

  Calvin C. Moore

• Mathematical Sciences Research Institute, Berkeley, USA

  Calvin C. Moore, Claude Schochet

• Department of Mathematics, Wayne State University, Detroit, USA

  Claude Schochet

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