Elements of KK-Theory

1. Front Matter

   Pages i-viii

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2. Hilbert C*-Modules

   • Kjeld Knudsen Jensen, Klaus Thomsen

   Pages 1-46

3. The Kasparov Approach to KK-Theory

   • Kjeld Knudsen Jensen, Klaus Thomsen

   Pages 47-92

4. C*-Extensions

   • Kjeld Knudsen Jensen, Klaus Thomsen

   Pages 93-119

5. The Kasparov Groups for Ungraded C*-Algebras

   • Kjeld Knudsen Jensen, Klaus Thomsen

   Pages 121-161

6. Cuntz’s Picture of KK-Theory

   • Kjeld Knudsen Jensen, Klaus Thomsen

   Pages 163-186

7. Back Matter

   Pages 187-202

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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.

• Invariant
• K-theory
• Morphism
• algebra
• homomorphism
• proof

• Department of Mathematics, University of Pennsylvania, Philadelphia, USA

  Kjeld Knudsen Jensen

• Matematisk Institut Ny Munkegade, Aarhus C, Denmark

  Klaus Thomsen