An introduction to K-theory for C*-algebras - Rørdam, M., (Mikael) (Cambridge University Press, 2000)
Includes bibliographical references (p. 231-233) and indexes
1. C*-algebra theory -- 2. Projections and unitary elements -- 3. The K0-group of a unital C*-algebra -- 4. The functor K0 -- 5. The ordered Abelian group K0(A) -- 6. Inductive limit C*-algebras -- 7. Classification of AF-algebras -- 8. The functor K1 -- 9. The index map -- 10. The higher K-functors -- 11. Bott periodicity -- 12. The six-term exact sequence -- 13. Inductive limits of dimension drop algebras
"Over the last 25 years K-theory has become an integrated part of the study of C*-algebras. This book gives an elementary introduction to this interesting and rapidly growing area of mathematics
Fundamental to K-theory is the association of a pair of Abelian groups, K0(A) and K1(A), to each C*-algebra A. These groups reflect the properties of A in many ways. This book covers the basic properties of the functors K0 and K1 and their interrelationship. Applications of the theory include Elliott's classification theorem for AF-algebras, and it is shown that each pair of countable Abelian groups arises as the K-groups of some C*-algebra."--pub. desc