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Zbl 0603.55015
Gouyon, Luce
Classes caractéristiques et fondamentales en cobordismes et K- théories. (Characteristic and fundamental classes in cobordisms and K- theory). (French)
[J] Bull. Soc. Math. Fr. 113, 475-506 (1985). ISSN 0037-9484

The author studies characteristic classes of real and complex vector bundles, with value in K-theory and KO-theory. He also studies natural transformations from complex cobordism and oriented cobordism to K-theory and KO-theory. The aim is to reduce questions to calculations with formal power series. He shows that complexification induces an isomorphism from KO(MSO(4n)) to K(MSO(4n)), and uses this result to study KO-theory characteristic classes of real vector bundles. \par These results appear to date from the early 1970's. One could also approach these problems with the help of formal group techniques, as presented by {\it J. F. Adams} in part 2 of his book [Stable homotopy and generalised homology (1974; Zbl 0309.55016)].
[P.Landweber]

MSC 2000:: *55R40 Homology of classifying spaces, characteristic classes
55R50 Stable classes of vector space bundles, K-theory
55N22 Bordism and cobordism theories, etc.
55N15 K-theory (algebraic topology)

Keywords: fundamental classes; characteristic classes; K-theory; KO-theory; complex cobordism; oriented cobordism; formal power series; KO(MSO(4n)); K(MSO(4n))

Citations: Zbl 0309.55016

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