K-Theory and C*-Algebras: A Friendly Approach

K-theory is often considered a complicated `specialist's' theory. This book is an introduction to the basics and provides detailed explanation of the various concepts required for a deeper understanding of the subject. Some familiarity with basic C*algebra theory is assumed and then follows a careful construction and analysis of the operator K-theory groups and proof of the results of K-theory, including Bott periodicity. Of specific interest to algebraists and geometrists, the book aims to give full instruction. No details are left out in the presentation and many instructive and generously hinted exercises are provided. Apart from K-theory, this book offers complete and self contained expositions of important advanced C*-algebraic constructions like tensor products, multiplier algebras and Hilbert modules.

1 - C*-algebras - a summary
2 - Multiplier algebras
3 - Extensions of C*-algebras
4 - Invertibles and unitaries
5 - Projections
6 - K0-basic properties
7 - K1 and suspensions
8 - The index map in K-theory
9 - Bott periodicity
10 - K-theory for multiplier algebras
11 - Homology
12 - Some examples: AF-algebras, Cuntz algebras, rotation algebras
13 - Vector bundles and topological K-theory
14 - The classical Fredholm index
15 - Hilbert modules
16 - The Kuiper-Mingo theorem
17 - A generalized Fredholm index
G - The Grothendieck group
L - Inductive limits
O - (Dis)order and positivity in C*-algebras
T - Tensor products -or: the importance of being subcross