K-Theory for Operator Algebras
K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applica...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1986, 1986
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| Edition: | 1st ed. 1986 |
| Series: | Mathematical Sciences Research Institute Publications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I. Introduction To K-Theory
- 1. Survey of topological K-theory
- 2. Overview of operator K-theory
- II. Preliminaries
- 3. Local Banach algebras and inductive limits
- 4. Idempotents and equivalence
- III. K0-Theory and Order
- 5. Basi K0-theory
- 6. Order structure on K0
- 7. Theory of AF algebras
- IV. K1-Theory and Bott Periodicity
- 8. Higher K-groups
- 9. Bott Periodicity
- V. K-Theory of Crossed Products
- 10. The Pimsner-Voiculescu exact sequence and Connes’ Thorn isomorphism
- 11. Equivariant K-theory
- VI. More Preliminaries
- 12. Multiplier algebras
- 13. Hilbert modules
- 14. Graded C*-algebras
- VII. Theory of Extensions
- 15. Basic theory of extensions
- 16. Brown-Douglas-Fillmore theory and other applications
- VIII. Kasparov’s KK-Theory
- 17. Basic theory
- 18. Intersection product
- 19. Further structure in KK-theory
- 20. Equivariant KK-theory
- IX. Further Topics
- 21. Homology and cohomology theories on C*-algebras
- 22. Axiomatic K-theory
- 23. Universal coefficient theorems and Künneth theorems
- 24. Survey of applications to geometry and topology