Elliptic theory and noncommutative geometry : nonlocal elliptic operators
Author(s)
Bibliographic Information
Elliptic theory and noncommutative geometry : nonlocal elliptic operators
（Operator theory : advances and applications, v. 183 . Advances in partial differential equations）
Birkhäuser, c2008
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. [217]-221) and index
Description and Table of Contents
Description
This comprehensive yet concise book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. This is the first book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. To make the book self-contained, the authors have included necessary geometric material.
Table of Contents
Preface.- Introduction.- I. Analysis of Nonlocal Elliptic Operators.- 1. Nonlocal Functions and Bundles.- 2. Nonlocal Elliptic Operators.- 3. Elliptic Operators over C*-Algebras.- II. Homotopy Invariants of Nonlocal Elliptic Operators.- 5. Analytic Invariants.- 6. Bott Periodicity.- 7. Direct Image and Index Formulas in K-Theory.- 8. Chern Character.- 9. Cohomological Index Formula.- 10. Cohomological Formula for the Lambda-Index.- 11. Index of Nonlocal Operators over C*-Algebras.- III. Examples.- 12. Index Formula on the Noncommutative Torus.- 13. An Application of Higher Traces.- 14. Index Formula for a Finite Group Gamma.- IV. Appendices.- A. C*-Algebras.- A.1 Basic Notions.- A.2 Representations of C*-Algebras.- A.3 Tensor Products and Nuclear Algebras.- B. K-Theory of Operator Algebras.- B.1 Covariant K-Theory.- B.2 K-Homology.- C. Cyclic Homology and Cohomology.- C.1 Cyclic Cohomology.- C.2 Cyclic Homology.- Concise Bibliographical Remarks.- Bibliography.- Index
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