9783540798897-3540798897-K-Theory: An Introduction (Classics in Mathematics)

K-Theory: An Introduction (Classics in Mathematics)

ISBN-13: 9783540798897
ISBN-10: 3540798897
Edition: 2008
Author: Karoubi, Max
Publication date: 2008
Publisher: Springer
Format: Paperback 334 pages
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Book details

ISBN-13: 9783540798897
ISBN-10: 3540798897
Edition: 2008
Author: Karoubi, Max
Publication date: 2008
Publisher: Springer
Format: Paperback 334 pages

Summary

Acknowledged authors Karoubi, Max wrote K-Theory: An Introduction (Classics in Mathematics) comprising 334 pages back in 2008. Textbook and eTextbook are published under ISBN 3540798897 and 9783540798897. Since then K-Theory: An Introduction (Classics in Mathematics) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

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".

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