Author | Rosenberg, Jonathan. author |
---|---|
Title | Algebraic K-Theory and Its Applications [electronic resource] / by Jonathan Rosenberg |
Imprint | New York, NY : Springer New York, 1994 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4314-4 |
Descript | X, 394 p. online resource |
1. K0 of Rings -- 1. Defining K0 -- 2. K0 from idempotents -- 3. K0 of PIDs and local rings -- 4. K0 of Dedekind domains -- 5. Relative K0 and excision -- 6. An application: Swanโs Theorem and topological K- theory -- 7. Another application: Euler characteristics and the Wall finiteness obstruction -- 2.K1 of Rings -- 1. Defining K1 -- 2. K1 of division rings and local rings -- 3. 1 of PIDs and Dedekind domains -- 4. Whitehead groups and Whitehead torsion -- 5. Relative K1 and the exact sequence -- 3. K0 and K1 of Categories, Negative K-Theory -- 1. K0 and K1 of categories, Go and G1 of rings -- 2. The Grothendieck and Bass-Heller-Swan Theorems -- 3. Negative K-theory -- 4. Milnorโs K2 -- 1. Universal central extensions and H2 -- 2. The Steinberg group -- 3. Milnorโs K2 -- 4. Applications of K2 -- 5. The +?Construction and Quillen K-Theory -- 1. An introduction to classifying spaces -- 2. Quillenโs +?construction and its basic properties -- 3. A survey of higher K-theory -- 6. Cyclic homology and its relation to K-Theory -- 1. Basics of cyclic homology -- 2. The Chern character -- 3. Some applications -- 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