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K-theory

Author: Michael Francis Atiyah; D W Anderson
Publisher: Boca Raton : CRC Press, 2018.
Series: Advanced book classics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 K-theory.The theory is taken as far  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michael Francis Atiyah; D W Anderson
ISBN: 9780429493546 0429493541
OCLC Number: 1028553031
Description: 1 online resource.
Series Title: Advanced book classics.
Responsibility: M.F. Atiyah ; notes by D.W. Anderson.

Abstract:

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 K-theory.The 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.

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