代數K理論及其應用(英文版)

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