K-Theory

An Introduction

  • Max Karoubi
Part of the Classics in Mathematics book series (CLASSICS)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Max Karoubi
    Pages 1-51
  3. Max Karoubi
    Pages 52-111
  4. Max Karoubi
    Pages 112-179
  5. Max Karoubi
    Pages 180-269
  6. Max Karoubi
    Pages 270-300
  7. Max Karoubi
    Pages 317-318
  8. Max Karoubi
    Pages 318-320
  9. Max Karoubi
    Pages 320-320
  10. Max Karoubi
    Pages 320-321
  11. Max Karoubi
    Pages 321-321
  12. Back Matter
    Pages 301-316

About this book

Introduction

From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch  con­sidered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. 
Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory.

The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".


Keywords

Algebraic topology Compact space Homotopy Homotopy group K-theory algebra applications of K-Theory homotopy theory topology vector bundle

Authors and affiliations

  • Max Karoubi
    • 1
  1. 1.U.E.R. de Mathématiques, Tour 45-55Université Paris VIIParis Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-79890-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1978
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-79889-7
  • Online ISBN 978-3-540-79890-3
  • Series Print ISSN 1431-0821
  • About this book