Abstract
In Chapter 4 we defined the notion of a fibre bundle (a locally trivial fibration); in this chapter we consider an important class of fibre bundles—those for which every fibre has the structure of a vector space in a way which is compatible on neighboring fibres. We show how equivalence classes of such vector bundles over a CW-complex can be used to define groups K*(X) in such a way that K* becomes a cohomology theory.
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References
J. F. Adams [2]
M. F. Atiyah [16]
M. F. Atiyah and F. Hirzebruch [18]
M. F. Atiyah and I. M. Singer [19]
J. M. Boardman and R. M. Vogt [22]
R. Bott [25]
D. Husemoller [49]
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© 2002 Springer-Verlag Berlin Heidelberg
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Switzer, R.M. (2002). Vector Bundles and K-Theory. In: Algebraic Topology — Homotopy and Homology. Classics in Mathematics, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61923-6_12
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DOI: https://doi.org/10.1007/978-3-642-61923-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42750-6
Online ISBN: 978-3-642-61923-6
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