Global Analysis on Foliated Spaces
By: by Calvin C. Moore, Claude Schochet
Contributors: Schochet, Claude
Series: Mathematical Sciences Research Institute Publications -- 9; Mathematical Sciences Research Institute publications -- 9.
Publisher: Springer New York
Published: 1988
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 337
ISBN-13: 9781461395942; 9781461395928
Subjects: Mathematics; Algebraic topology
Description: This book develops a variety of aspects of analysis and geometry on foliated spaces which should be useful in many situations. These strands are then brought together to provide a context and to expose Connes` index theorem for foliated spaces, a theorem which asserts the equality of the analytic and the topological index (two real numbers) which are associated to a tangentially elliptic operator. An additional purpose of this exposition is preparing the way towards the more general index theorem of Connes and Skandalis. This index theorem describes the abstract index class in KO (CR*(G(M))), the index group of the C*-algebra of the foliated space, and is necessarily substantially more abstract, while the tools used here are relatively elementary and straightforward, and are based on the heat equation method.
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Table of contents: title: Introduction; title: Locally Traceable Operators; title: Foliated Spaces; title: Tangential Cohomology; title: Transverse Measures; title: Characteristic Classes; title: Operator Algebras; title: Pseudodifferential Operators; title: The Index Theorem; title: Appendices: A: The operator. B: L2 Harmonic Forms on Non-Compact Manifolds. C: Positive Scalar Curvature Along the Leaves; title: References.