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Cover: 9783540798897 | K-Theory | An Introduction | Max Karoubi | Taschenbuch | xviii | 2008
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K-Theory
An Introduction
Taschenbuch von Max Karoubi
Sprache: Englisch

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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 [...] this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".
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 [...] this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".
Über den Autor

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.

Zusammenfassung

Recognized classics and standard reference for the subject

Inhaltsverzeichnis
Vector Bundles.- First Notions of K-Theory.- Bott Periodicity.- Computation of Some K-Groups.- Some Applications of K-Theory.- Vector Bundles.- First Notions of K-Theory.- Bott Periodicity.- Computation of Some K-Groups.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xviii
316 S.
ISBN-13: 9783540798897
ISBN-10: 3540798897
Sprache: Englisch
Herstellernummer: 12267408
Einband: Kartoniert / Broschiert
Autor: Karoubi, Max
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 19 mm
Von/Mit: Max Karoubi
Erscheinungsdatum: 18.09.2008
Gewicht: 0,517 kg
Artikel-ID: 101791853
Über den Autor

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.

Zusammenfassung

Recognized classics and standard reference for the subject

Inhaltsverzeichnis
Vector Bundles.- First Notions of K-Theory.- Bott Periodicity.- Computation of Some K-Groups.- Some Applications of K-Theory.- Vector Bundles.- First Notions of K-Theory.- Bott Periodicity.- Computation of Some K-Groups.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xviii
316 S.
ISBN-13: 9783540798897
ISBN-10: 3540798897
Sprache: Englisch
Herstellernummer: 12267408
Einband: Kartoniert / Broschiert
Autor: Karoubi, Max
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 19 mm
Von/Mit: Max Karoubi
Erscheinungsdatum: 18.09.2008
Gewicht: 0,517 kg
Artikel-ID: 101791853
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