Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T08:55:00.131Z Has data issue: false hasContentIssue false
  • English
  • Français

Sums of stably trivial vector bundles

Published online by Cambridge University Press:  24 October 2008

Jacques Allard
Jacques Allard
Affiliation:
Département de Mathématiques, Université de Montréal, Montreal, Canada
Get access Rights & Permissions [Opens in a new window]

Extract

We say that a real vector bundle ξ over a finite C.W. complex X is stably trivial of type (n, k) or, simply, of type (n, k) if ξ ⊕ kε ≅ nε, where ε denotes a trivial line bundle. The following theorem is an immediate corollary (see (12)) of a theorem of T. Y. Lam ((9), theorem 2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 1 , January 1980 , pp. 97 - 107
Copyright
Copyright © Cambridge Philosophical Society 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Allard, J. Contribution to the theory of stably trivial vector bundles. Ph.D. thesis, University of British Columbia, 1977.Google Scholar
(2)Atiyah, M. F.Vector bundles and the Kunneth formula. Topology 1 (1962), 245–248.CrossRefGoogle Scholar
(3)Crabb, M. C. and Sutherland, W. A.A bundle over the tangent sphere-bundle of a π- manifold. Quart. J. Math. Oxford (in the Press).Google Scholar
(4)Gitler, S. and Lam, K. Y.The K-theory of Stiefel manifolds; the Steenrod algebra and its applications. Lecture Notes in Mathematics, no. 168 (Springer, 1970).Google Scholar
(5)Husemoller, D.Fiber bundles, 2nd ed. (New York, Springer-Verlag, 1976).Google Scholar
(6)James, I. M.The intrinsic join. Proc. London Math. Soc. 8 (1958), 507–535.CrossRefGoogle Scholar
(7)Kervaire, M., Some non stable homotopy groups of Lie groups. Illinois J. Math. 4 (1960), 161–169.CrossRefGoogle Scholar
(8)Lam, K. Y.A formula for the tangent bundle of the flag manifolds and related manifolds. Trans. Amer. Math. Soc. 213 (1975), 305–311.CrossRefGoogle Scholar
(9)Lam, T. Y.Series summation of stably free modules. Quart. J. Math. Oxford (2), 27 (1976), 37–46.CrossRefGoogle Scholar
(10)Steenrod, N. E. and Epstein, D. B. A. Cohomology operations, Ann. of Math. Study 50 (Princeton, 1962).Google Scholar
(11)Sutherland, W. A.A note on the parallelisability of sphere bundles over spheres. J. London Math. Soc. 39 (1964), 55–62.CrossRefGoogle Scholar
(12)Swan, R.Vector bundles and projective modules. Trans. Amer. Math. Soc. 105 (1962), 264–267.CrossRefGoogle Scholar
(13)Whitehead, G. W.Note on cross sections in Stiefel manifolds. Comment. Math. Helv. 37 (1963), 239–240.Google Scholar