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Algebraic K-Theory and Its Applications

Author: Jonathan Rosenberg
Publisher: New York, NY : Springer New York, 1994.
Series: Graduate texts in mathematics, 147.
Edition/Format:   eBook : Bibliographic data : English
Summary:
Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Bibliographic data, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jonathan Rosenberg
ISBN: 9781461243144 1461243149 9781461287353 1461287359
OCLC Number: 840279648
Description: 1 online resource (x, 408 pages 2 illustrations)
Contents: 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: Swan's 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. Milnor's K2 --
1. Universal central extensions and H2 --
2. The Steinberg group --
3. Milnor's K2 --
4. Applications of K2 --
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 --
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.
Series Title: Graduate texts in mathematics, 147.
Responsibility: by Jonathan Rosenberg.

Abstract:

Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. Topics include algebraic topology,  Read more...

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