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On Chern classes of stably fibre homotopic trivial bundles

Published online by Cambridge University Press:  18 May 2009

L. Astey ,
S. Gitler ,
E. Micha  and
G. Pastor
L. Astey
Affiliation:
Department of Mathematics, Centro de Investigacion del IPN, Apartado Postal 14-740, Mexico07000 D.F.
S. Gitler
Affiliation:
Department of Mathematics, Centro de Investigacion del IPN, Apartado Postal 14-740, Mexico07000 D.F.
E. Micha
Affiliation:
Department of Mathematics, Centro de Investigacion del IPN, Apartado Postal 14-740, Mexico07000 D.F.
G. Pastor
Affiliation:
Department of Mathematics, Centro de Investigacion del IPN, Apartado Postal 14-740, Mexico07000 D.F.
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 2 , May 1988 , pp. 213 - 214
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

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