Preface Chapter 1. Ko of Rings 1. Defining K0 2. Ko from idempotents 3. Ko of PIDs and local rings 4. Ko of Dedekind domains 5. Relative Ko and excision 6. An application: Swan's Theorem and topological K- theory 7. Another application: Euler characteristics and the Wall finiteness obstruction Chapter 2. K1 of Rings 1. Defining K1 2. K1 of division rings and local rings 3. K1 of PIDs and Dedekind domains 4. Whitehead groups and Whitehead torsion 5. Relative K1 and the exact sequence Chapter 3. Ko and K1 of Categories, Negative K-Theory 1. Ko and K1 of categories, Go and G1 of rings 2. The Grothendieck and Bass-Heller-Swan Theorems 3. Negative K-theory Chapter 4. Milnor's K2 1. Universal central extensions and H2 Universal central extensions Homology of groups 2. The Steinberg group 3. Milnor's K2 4. Applications of K2 Computing certain relative K1 groups K2 of fields and number theory Almost commuting operators Pseudo-isotopy Chapter 5. The +-Construction and Quillen K-Theory 1. An introduction to classifying spaces 2. Quillen's +-construction and its basic properties 3. A survey of higher K-theory Products K-theory of fields and of rings of integers The Q-construction and results proved with it Applications Chapter 6. Cyclic homology and its relation to K-Theory 1. Basics of cyclic homology Hochschild homology Cyclic homology Connections with "non-commutative de Rhom theory" 2. The Chern character The classical Chern character The Chern character on Ko The Chern character on higher K-theory 3. Some applications Non-vanishing of class groups and Whitehead groups Idempotents in C*-algebras Group rings and assembly maps References Books and Monographs on Related Areas of Algebra,Analysis, Number Theory, and Topology Books and Monographs on Algebraic K-Theory Specialized References Notational Index Subject Index
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