K-Theory for Operator Algebras / by Bruce Blackadar
(Mathematical Sciences Research Institute Publications ; 5)
| データ種別 | 電子ブック |
|---|---|
| 出版情報 | New York, NY : Springer New York , 1986 |
| 本文言語 | 英語 |
| 大きさ | VII, 337 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text |
| 著者標目 | *Blackadar, Bruce author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebraic topology FREE:Mathematics FREE:Algebraic Topology |
| 分 類 | DC23:514.2 |
| 巻冊次 | ISBN:9781461395720 
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| ISBN | 9781461395720 |
| URL | http://dx.doi.org/10.1007/978-1-4613-9572-0 |
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