Hostname: page-component-848d4c4894-mwx4w Total loading time: 0 Render date: 2024-07-04T17:09:19.459Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1.Adams, J. F., Stable homotopy and generalised homology (University of Chicago Press, 1974).Google Scholar
2.Atiyah, M. F., Thorn complexes, Proc. London Math. Soc. (3) 11 (1961), 291–310.CrossRefGoogle Scholar
3.Milnor, J. W., Characteristic classes (Princeton University Press, 1974).CrossRefGoogle Scholar
4.Quillen, D., Elementary proofs of some results of cobordism theory using Steenrod operations, Adv. in Math. 7 (1971), 29–56.CrossRefGoogle Scholar