Handbook of K-theory

Eric Friedlander, Daniel R. Grayson9783540230199, 354023019X

This handbook presents the first compilation of techniques and results across much of the present state of the art in K-theory. Consisting of individual chapters, each an exposition of a particular subfield or line of development related to K-theory, written by an expert, it outlines fundamental ideas and techniques of the past, fundamental open problems, and exciting directions for future research. Much of the material presented here appears for the first time in book form. The intent of each chapter is present to the interested reader, be she an established K-theorist or someone interested in obtaining an overview of results, an exposition of both results and techniques in the literature as well as challenges for the future. The book should be especially useful for students and mathematicians interested in pursuing further research in this rapidly expanding field.

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Table of contents :
Cover Page……Page 1
Title Page – Volume 1……Page 3
ISBN 354023019X Springer Berlin Heidelberg New York……Page 4
Preface……Page 5
Table of Contents – Volume 1……Page 9
Table of Contents – Volume 2……Page 11
List of Contributors……Page 13
Part I Foundations and Computations……Page 15
Deloopings in Algebraic K-Theory……Page 17
The Motivic Spectral Sequence……Page 53
K-Theory of Truncated Polynomial Algebras……Page 85
Bott Periodicity in Topological, Algebraic and Hermitian K-Theory……Page 125
Algebraic K-Theory of Rings of Integers in Local and Global Fields……Page 153
Part II K-Theory and Algebraic Geometry……Page 205
Motivic Cohomology, K-Theory and Topological Cyclic Homology……Page 207
K-Theory and Intersection Theory……Page 249
Regulators……Page 309
Algebraic K-Theory, Algebraic Cycles and Arithmetic Geometry……Page 365
Mixed Motives……Page 443
Title Page – Volume 2……Page 550
Part III K-Theory and Geometric Topology……Page 551
Witt Groups……Page 553
K-Theory and Geometric Topology……Page 591
Quadratic K-Theory and Geometric Topology……Page 625
Part IV K-Theory and Operator Algebras……Page 667
Bivariant K- and CyclicTheories……Page 669
The Baum–Connes and the Farrell–Jones Conjectures in K- andL-Theory……Page 717
Comparison BetweenAlgebraic and Topological K-Theory for Banach Algebras and C- Algebras*……Page 857
Part V Other Forms of K-Theory……Page 889
Semi-topological K-Theory……Page 891
Equivariant K-Theory……Page 939
K(1)-Local Homotopy Theory, Iwasawa Theory and Algebraic K-Theory……Page 969
The K-Theory of Triangulated Categories……Page 1025
Appendix Bourbaki Articles on the Milnor Conjecture……Page 1093
Motivic Complexes of Suslin and Voevodsky……Page 1095
La conjecture de Milnor (d’après V. Voevodsky)……Page 1119
B……Page 1165
C……Page 1166
E……Page 1168
G……Page 1169
H……Page 1170
K……Page 1171
M……Page 1172
P……Page 1173
R……Page 1174
S……Page 1175
V……Page 1176
Z……Page 1177