Author | Jensen, Kjeld Knudsen. author |
---|---|

Title | Elements of KK-Theory [electronic resource] / by Kjeld Knudsen Jensen, Klaus Thomsen |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1991 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-0449-7 |

Descript | VIII, 202 p. online resource |

SUMMARY

The KK-theory of Kasparov is now approximately twelve years old; its power, utility and importance have been amply demonstrated. Nonetheยญ 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 difficulยญ 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 presenยญ tation of the very basic elements of the theory, the functoriality of the KK-groups, and the Kasparov product

CONTENT

1. Hilbert C*- Modules -- ยง 1.1. Hilbert C*-Modules and Multiplier Algebras -- ยง 1.2. Constructions with Hilbert B-Modules -- ยง 1.3. Stable C*-Algebras -- 2. The Kasparov Approach to KK-Theory -- ยง 2.1. The KK-Groups -- ยง 2.2. The Kasparov Product -- 3. C*-Extensions -- ยง 3.1. The Busby Invariant -- ยง 3.2. The Extension Groups -- ยง 3.3. Connections to KK-Theory -- 4. The Kasparov Groups for Ungraded C*-Algebras -- ยง 4.1. From Hilbert C*-Modules to *-Homomorphisms -- ยง 4.2. Split-Exactness of KKh -- ยง 4.3. The Kasparov Product as a Generalization of Composition of *-Homomorphisms -- 5. Cuntzโ{128}{153}s Picture of KK-Theory -- ยง 5.1. qA -- ยง 5.2. KKc(A, B) ? KKo(A, B) -- References

Mathematics
Algebra
Category theory (Mathematics)
Homological algebra
K-theory
Mathematics
K-Theory
Category Theory Homological Algebra
Algebra