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© 1978

K-Theory

An Introduction

Benefits

  • Recognized classics and standard reference for the subject

Book

Part of the Classics in Mathematics book series

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 317-321
  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

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

About the authors

Max Karoubi received his PhD in mathematics (Doctorat d'Etat) from Paris University in 1967, while working in the CNRS (Centre National de la Recherche Scientifique), under the supervision of Henri Cartan and Alexander Grothendieck.  After his PhD, he took a position of "Maître de Conférences" at the University of Strasbourg until 1972. He was then nominated full Professor at the University of Paris 7-Denis Diderot until 2007. He is now an Emeritus Professor there.

Bibliographic information

  • Book Title K-Theory
  • Book Subtitle An Introduction
  • Authors Max Karoubi
  • Series Title Classics in Mathematics
  • 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 Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-540-08090-9
  • Softcover ISBN 978-3-540-79889-7
  • eBook ISBN 978-3-540-79890-3
  • Series ISSN 1431-0821
  • Series E-ISSN 2512-5257
  • Edition Number 1
  • Number of Pages XVIII, 316
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as volume 226 in the series: Grundlehren der Mathematischen Wissenschaften
  • Topics K-Theory
    Algebraic Topology
  • Buy this book on publisher's site

Reviews

From the reviews:

"Karoubi’s classic K-Theory, An Introduction … is ‘to provide advanced students and mathematicians in other fields with the fundamental material in this subject’. … K-Theory, An Introduction is a phenomenally attractive book: a fantastic introduction and then some. … serve as a fundamental reference and source of instruction for outsiders who would be fellow travelers." (Michael Berg, MAA Online, December, 2008)