Elements of KK-Theory

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

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 traditionall...

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Bibliographic Details
Main Authors: Jensen, Kjeld Knudsen (Author), Thomsen, Klaus (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 1991.
Edition:1st ed. 1991.
Series:Mathematics: Theory & Applications
Springer eBook Collection.
Subjects:
K-theory.
Category theory (Mathematics).
Homological algebra.
Algebra.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.

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