LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	514.2
Title	K-Theory for Operator Algebras ([EBook]) / by Bruce Blackadar.
Author	Blackadar, Bruce
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1986.
Physical Details	VII, 337 pages : online resource.
Series	Mathematical Sciences Research Institute publications 0940-4740 ; ; 5
ISBN	9781461395720
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4613-9572-0
Links to Related Works	Subject References: Algebraic Topology . K-Theory . Operator algebras . Authors: Blackadar, Bruce . Corporate Authors: SpringerLink (Online service) . Series: Mathematical Sciences Research Institute publications . Classification: 514.2 .

Catalogue Display

K-Theory for Operator Algebras

Reviews