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代数K理论及其应用 英文版PDF|Epub|txt|kindle电子书版本下载
- JonathanRosenberg著 著
- 出版社： 世界图书北京出版公司
- ISBN：9787510005145
- 出版时间：2010
- 标注页数：394页
- 文件大小：19MB
- 文件页数：404页
- 主题词：代数K理论－英文
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图书目录
Chapter 1．K0 of Rings1
1．Defining K01
2．K0 from idempotents7
3．K0 of PIDs and local rings11
4．K0 of Dedekind domains16
5．Relative K0 and excision27
6．An application:Swan's Theorem and topological K-theory32
7．Another application:Euler characteristics and the Wall finiteness obstruction41
Chapter 2．K1 of Rings59
1．Defining K159
2．K1 of division rings and local rings62
3．K1 of PIDs and Dedekind domains74
4．Whitehead groups and Whitehead torsion83
5．Relative K1 and the exact sequence92
Chapter 3．K0 and K1 of Categories,Negative K-Theory108
1．K0 and K1 of categories,G0 and G1 of rings108
2．The Grothendieck and Bass-Heller-Swan Theorems132
3．Negative K-theory153
Chapter 4．Milnor's K2162
1．Universal central extensions and H2162
Universal central extensions163
Homology of groups168
2．The Steinberg group187
3．Milnor's K2199
4．Applications of K2218
Computing certain relative K1 groups218
K2 of fields and number theory221
Almost commuting operators237
Pseudo-isotopy240
Chapter 5．The+-Construction and Quillen K-Theory245
1．An introduction to classifying spaces245
2．Quillen's+-construction and its basic properties265
3．A survey of higher K-theory279
Products279
K-theory of fields and of rings of integers281
The Q-construction and results proved with it289
Applications295
Chapter 6．Cyclic homology and its relation to K-Theory302
1．Basics of cyclic homology302
Hochschild homology302
Cyclic homology306
Connections with"non-commutative de Rham theory"325
2．The Chern character331
The classical Chern character332
The Chern character on K0335
The Chern character on higher K-theory340
3．Some applications350
Non-vanishing of class groups and Whitehead groups350
Idempotents in C*-algebras355
Group rings and assembly maps362
References369
Books and Monographs on Related Areas of Algebra,Analysis,Number Theory,and Topology369
Books and Monographs on Algebraic K-Theory371
Specialized References372
Notational Index377
Subject Index383