Elements Of Kk Theory
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Elements of KK-Theory
Author: Kjeld Knudsen Jensen
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The KK-theory of Kasparov is now approximately twelve years old; its power, utility and importance have been amply demonstrated. Nonethe less, it remains a forbiddingly difficult topic with which to work and learn. There are many reasons for this. For one thing, KK-theory spans several traditionally disparate mathematical regimes. For another, the literature is scattered and difficult to penetrate. Many of the major papers require the reader to supply the details of the arguments based on only a rough outline of proofs. Finally, the subject itself has come to consist of a number of difficult segments, each of which demands prolonged and intensive study. is to deal with some of these difficul Our goal in writing this book ties and make it possible for the reader to "get started" with the theory. We have not attempted to produce a comprehensive treatise on all aspects of KK-theory; the subject seems too vital to submit to such a treatment at this point. What seemed more important to us was a timely presen tation of the very basic elements of the theory, the functoriality of the KK-groups, and the Kasparov product.
K-Theory for Operator Algebras
Author: Bruce Blackadar
language: en
Publisher: Cambridge University Press
Release Date: 1998-09-13
This book is the only comprehensive treatment of K-theory for operator algebras.
K-Theory for Operator Algebras
Author: Bruce Blackadar
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
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.