代數K理論及其應用（簡體書）

代數K理論在代數拓撲、數論、代數幾何和算子理論等現代數學各個領域中的作用越來越大。這門學科的廣泛性往往使人感覺望而生畏。本書以1990年秋天Maryland大學講義為基礎，不僅為數學領域研究生提供很好的學習代數K理論的基本知識，也講述其在各個領域的應用。全書結構完整，了解代數基礎知識、基本代數拓撲和幾何拓撲知識就可以完全讀懂這本書。該書也涉及到不少代數拓撲、拓撲代數和代數數論的知識。最后一章簡明地介紹了循環同調以及其與K理論的關係。目次：環的K0群；環的K1群；范疇的K0、K1群，MilnorK2群；QuillenK理論和+-結構；循環同調及其與K理論的關係。
讀者對象：數學系高年級學生及研究生的教材，也可供高校數學教師及數學研究人員閱讀或參考。

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: Swans 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. Milnors K2
　1. Universal central extensions and H2
　Universal central extensions
　Homology of groups
　2. The Steinberg group
　3. Milnors 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. Quillens +-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