Elements of KK-Theory - Kjeld Knudsen Jensen, Klaus Thomsen

Elements of KK-Theory

Buch | Softcover
202 Seiten
2012 | Softcover reprint of the original 1st ed. 1991
Humana Press Inc. (Verlag)
978-1-4612-6765-2 (ISBN)
106,99 inkl. MwSt
The KK-theory of Kasparov is now approximately twelve years old; Nonethe­ less, it remains a forbiddingly difficult topic with which to work and learn. Finally, the subject itself has come to consist of a number of difficult segments, each of which demands prolonged and intensive study.
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.

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.

Reihe/Serie Mathematics: Theory & Applications
Zusatzinfo VIII, 202 p.
Verlagsort Totowa, NJ
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 1-4612-6765-X / 146126765X
ISBN-13 978-1-4612-6765-2 / 9781461267652
Zustand Neuware
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