代数K理论及其应用 英文版PDF电子书下载

Chapter 1．K0 of Rings 1

1．Defining K0 1

2．K0 from idempotents 7

3．K0 of　PIDs and local rings 11

4．K0 of Dedekind domains 16

5．Relative K0 and excision 27

6．An application:Swan's Theorem and topological K-theory 32

7．Another application:Euler characteristics and the Wall finiteness obstruction 41

Chapter 2．K1 of Rings 59

1．Defining K1 59

2．K1 of division rings and local rings 62

3．K1 of PIDs and Dedekind domains 74

4．Whitehead groups and Whitehead torsion 83

5．Relative K1 and the exact sequence 92

Chapter 3．K0 and K1 of Categories,Negative K-Theory 108

1．K0 and K1 of categories,G0 and G1 of rings 108

2．The Grothendieck and Bass-Heller-Swan Theorems 132

3．Negative K-theory 153

Chapter 4．Milnor's K2 162

1．Universal central extensions and H2 162

Universal central extensions 163

Homology of groups 168

2．The Steinberg group 187

3．Milnor's K2 199

4．Applications of K2 218

Computing certain relative K1 groups 218

K2 of fields and number theory 221

Almost commuting operators 237

Pseudo-isotopy 240

Chapter 5．The+-Construction and Quillen K-Theory 245

1．An introduction to classifying spaces 245

2．Quillen's+-construction and its basic properties 265

3．A survey of higher K-theory 279

Products 279

K-theory of fields and of rings of integers 281

The Q-construction and results proved with it 289

Applications 295

Chapter 6．Cyclic homology and its relation to K-Theory 302

1．Basics of cyclic homology 302

Hochschild homology 302

Cyclic homology 306

Connections with"non-commutative de Rham theory" 325

2．The Chern character 331

The classical Chern character 332

The Chern character on K0 335

The Chern character on higher K-theory 340

3．Some applications 350

Non-vanishing of class groups and Whitehead groups 350

Idempotents in C*-algebras 355

Group rings and assembly maps 362

References 369

Books and Monographs on Related Areas of Algebra,Analysis,Number Theory,and Topology 369

Books and Monographs on Algebraic K-Theory 371

Specialized References 372

Notational Index 377

Subject Index 383