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Elements of KK-Theory

  • Kartonierter Einband
  • 216 Seiten
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The KK-theory of Kasparov is now approximately twelve years old; its power, utility and importance have been amply demonstrated. N... Weiterlesen
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Beschreibung

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.

Inhalt

1. Hilbert C*- Modules.- § 1.1. Hilbert C*-Modules and Multiplier Algebras.- § 1.2. Constructions with Hilbert B-Modules.- § 1.3. Stable C*-Algebras.- 2. The Kasparov Approach to KK-Theory.- § 2.1. The KK-Groups.- § 2.2. The Kasparov Product.- 3. C*-Extensions.- § 3.1. The Busby Invariant.- § 3.2. The Extension Groups.- § 3.3. Connections to KK-Theory.- 4. The Kasparov Groups for Ungraded C*-Algebras.- § 4.1. From Hilbert C*-Modules to *-Homomorphisms.- § 4.2. Split-Exactness of KKh.- § 4.3. The Kasparov Product as a Generalization of Composition of *-Homomorphisms.- 5. Cuntz's Picture of KK-Theory.- § 5.1. qA.- § 5.2. KKc(A, B) ? KKo(A, B).- References.

Produktinformationen

Titel: Elements of KK-Theory
Autor:
EAN: 9781461267652
ISBN: 146126765X
Format: Kartonierter Einband
Anzahl Seiten: 216
Gewicht: 335g
Größe: H235mm x B155mm x T11mm
Jahr: 2012
Auflage: Softcover reprint of the original 1st ed. 1991