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K-Theory

An Introduction

  • Book
  • © 1978

Overview

Authors:
  1. Max Karoubi

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

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  • Recognized classics and standard reference for the subject

Part of the book series: Classics in Mathematics (CLASSICS)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. Vector Bundles

    • Max Karoubi
    Pages 1-51

  3. First Notions of K-Theory

    • Max Karoubi
    Pages 52-111

  4. Bott Periodicity

    • Max Karoubi
    Pages 112-179

  5. Computation of Some K-Groups

    • Max Karoubi
    Pages 180-269

  6. Some Applications of K-Theory

    • Max Karoubi
    Pages 270-300

  7. Erratum

    • Max Karoubi
    Pages 321-321

  8. Erratum to: K-Theory

    • Max Karoubi
    Pages 317-321

  9. First Notions of K-Theory

    • Max Karoubi
    Pages 318-320

  10. Computation of Some K-Groups

    • Max Karoubi
    Pages 320-321

  11. Bott Periodicity

    • Max Karoubi
    Pages 320-320

  12. Back Matter

    Pages 301-316
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Keywords

About this book

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".




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)

Authors and Affiliations

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

    Max Karoubi

About the author

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

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1978

  • Softcover ISBN: 978-3-540-79889-7Published: 18 September 2008

  • eBook ISBN: 978-3-540-79890-3Published: 27 November 2009

  • Series ISSN: 1431-0821

  • Series E-ISSN: 2512-5257

  • Edition Number: 1

  • Number of Pages: XVIII, 316

  • Additional Information: Originally published as volume 226 in the series: Grundlehren der Mathematischen Wissenschaften

  • Topics: K-Theory, Algebraic Topology

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