Name: K-Theory
ISBN: 978-3-540-79890-3

Authors:

Max Karoubi ⁰

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

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Table of contents (10 chapters)

Front Matter

Pages I-XVIII

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Vector Bundles
- Max Karoubi
Pages 1-51
First Notions of K-Theory
- Max Karoubi
Pages 52-111
Bott Periodicity
- Max Karoubi
Pages 112-179
Computation of Some K-Groups
- Max Karoubi
Pages 180-269
Some Applications of K-Theory
- Max Karoubi
Pages 270-300
Erratum to: K-Theory
- Max Karoubi
Pages 317-321
First Notions of K-Theory
- Max Karoubi
Pages 318-320
Bott Periodicity
- Max Karoubi
Pages 320-320
Computation of Some K-Groups
- Max Karoubi
Pages 320-321
Erratum
- Max Karoubi
Pages 321-321
Back Matter

Pages 301-316

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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".

Keywords

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

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
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
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