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Cover: 9780201407921 | K-theory | Michael Atiyah | Taschenbuch | Einband - flex.(Paperback)
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K-theory
Taschenbuch von Michael Atiyah
Sprache: Englisch

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Beschreibung
These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of [...] theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism. In addition to the lecture notes proper, two papers of mine published since 1964 have been reproduced at the end. The first, dealing with operations, is a natural supplement to the material in Chapter III. It provides an alternative approach to operations which is less slick but more fundamental than the Grothendieck method of Chapter III, and it relates operations and filtration. Actually, the lectures deal with compact spaces, not cell-complexes, and so the skeleton-filtration does not figure in the notes. The second paper provides a new approach to K-theory and so fills an obvious gap in the lecture notes.
These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of [...] theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism. In addition to the lecture notes proper, two papers of mine published since 1964 have been reproduced at the end. The first, dealing with operations, is a natural supplement to the material in Chapter III. It provides an alternative approach to operations which is less slick but more fundamental than the Grothendieck method of Chapter III, and it relates operations and filtration. Actually, the lectures deal with compact spaces, not cell-complexes, and so the skeleton-filtration does not figure in the notes. The second paper provides a new approach to K-theory and so fills an obvious gap in the lecture notes.
Über den Autor
Michael Atiyah
Inhaltsverzeichnis
Vector Bundles * Basic definitions * Operations on vector bundles * Sub-bundles and quotient bundles * Vector bundles on compact spaces * Additional structures * G-bundles over G-spaces K-Theory * Definitions * Elementary properties * The Bott periodicity theorem * Kg(X) * Computations of K*(X) for some X * Multiplication in K*(X,Y) * The Thom isomorphism Operations * Exterior powers * The Adams operations * The group J(X) * Reprint: Power operations in K-Theory * Reprint: K-Theory and reality
Details
Erscheinungsjahr: 1994
Fachbereich: Allgemeines
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Taschenbuch
Inhalt: Einband - flex.(Paperback)
ISBN-13: 9780201407921
ISBN-10: 0201407922
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Atiyah, Michael
Hersteller: CRC Press
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 229 x 152 x 13 mm
Von/Mit: Michael Atiyah
Erscheinungsdatum: 01.05.1994
Gewicht: 0,354 kg
Artikel-ID: 128410778
Über den Autor
Michael Atiyah
Inhaltsverzeichnis
Vector Bundles * Basic definitions * Operations on vector bundles * Sub-bundles and quotient bundles * Vector bundles on compact spaces * Additional structures * G-bundles over G-spaces K-Theory * Definitions * Elementary properties * The Bott periodicity theorem * Kg(X) * Computations of K*(X) for some X * Multiplication in K*(X,Y) * The Thom isomorphism Operations * Exterior powers * The Adams operations * The group J(X) * Reprint: Power operations in K-Theory * Reprint: K-Theory and reality
Details
Erscheinungsjahr: 1994
Fachbereich: Allgemeines
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Taschenbuch
Inhalt: Einband - flex.(Paperback)
ISBN-13: 9780201407921
ISBN-10: 0201407922
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Atiyah, Michael
Hersteller: CRC Press
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 229 x 152 x 13 mm
Von/Mit: Michael Atiyah
Erscheinungsdatum: 01.05.1994
Gewicht: 0,354 kg
Artikel-ID: 128410778
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