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Table of contents

  1. Front Matter
    Pages I-XIV
  2. Foundations and Computations

    1. Front Matter
      Pages 1-1
    2. Gunnar Carlsson
      Pages 3-37
    3. Daniel R. Grayson
      Pages 39-69
    4. Lars Hesselholt
      Pages 71-110
  3. K-Theory and Algebraic Geometry

    1. Front Matter
      Pages 191-191
    2. Henri Gillet
      Pages 235-293
    3. Alexander B. Goncharov
      Pages 295-349
    4. Marc Levine
      Pages 429-521
  4. K-Theory and Geometric Topology

    1. Front Matter
      Pages 537-537
    2. Paul Balmer
      Pages 539-576
    3. Jonathan Rosenberg
      Pages 577-610
    4. Bruce Williams
      Pages 611-651
  5. K-Theory and Operator Algebras

    1. Front Matter
      Pages 653-653
    2. Joachim Cuntz
      Pages 655-702
  6. Other Forms of K-Theory

    1. Front Matter
      Pages 875-875
    2. Eric M. Friedlander, Mark E. Walker
      Pages 877-924
    3. Alexander S. Merkurjev
      Pages 925-954
    4. Amnon Neeman
      Pages 1011-1078
  7. Back Matter
    Pages 1151-1163

About this book

Introduction

This handbook offers a compilation of techniques and results in K-theory.

These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. The overall intent of this handbook is to offer the interested reader an exposition of our current state of knowledge as well as an implicit blueprint for future research. This handbook should be especially useful for students wishing to obtain an overview of K-theory and for mathematicians interested in pursuing challenges in this rapidly expanding field.

Keywords

Algebraic K-theory MSC (2000):19-XX algebraic geometry algebraic number theory arithmetric geometry geometric topology motivic cohomology topological k-theory

Editors and affiliations

  • Eric M. Friedlander
    • 1
  • Daniel R. Grayson
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information