Geodesic
On Chern classes of stably fibre homotopic trivial bundles
Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 213-214

Voir la notice de l'article provenant de la source Cambridge University Press

Let ξ be a stably fibre homotopic trivial vector bundle. A classical result of Thorn states that the Stiefel-Whitney classes of ξ vanish, and one way to prove this is as follows. Let u be the Thorn class of ξ in mod 2 cohomology. Then u is stably spherical by [2] and therefore all stable cohomology operations vanish on u, showing that wi(ξ)u = Sqiu = 0. In this note we shall apply this same method using complex cobordism and Landweber-Novikov operations to study relations among Chern classes of a stably fibre homotopic trivial complex vector bundle. We will thus obtain in a unified way certain strong mod p conditions for every prime p. 
Astey, L.; Gitler, S.; Micha, E.; Pastor, G. On Chern classes of stably fibre homotopic trivial bundles. Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 213-214. doi: 10.1017/S0017089500007242
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[3] 3.Milnor, J. W., Characteristic classes (Princeton University Press, 1974). Google Scholar | DOI

[4] 4.Quillen, D., Elementary proofs of some results of cobordism theory using Steenrod operations, Adv. in Math. 7 (1971), 29–56. Google Scholar | DOI

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