Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-01T21:08:54.760Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Stable Homotopy Type of Thom Complexes

Published online by Cambridge University Press:  20 November 2018

R. P. Held  and
D. Sjerve
R. P. Held
Affiliation:
University of British Columbia, Vancouver, British Columbia
D. Sjerve
Affiliation:
University of British Columbia, Vancouver, British Columbia
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 α be a real vector bundle over a finite CW complex X and let T(α;X) be its associated Thorn complex. We propose to study the S-type (stable homotopy type) of Thorn complexes in the framework of the Atiyah-Adams J-Theory. Therefore we focus our attention on the group JR(X) which is defined to be the group of orthogonal sphere bundles over X modulo stable fiber homotopy equivalence.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1285 - 1294
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Adams, J. F., On the groups J(X), II, Topology 3 (1965), 137–171.Google Scholar
2. Adams, J. F. and Walker, G., On complex stiefel manifolds, Proc. Cambridge Phil. Soc. 61 (1965), 81–103.Google Scholar
3. Atiyah, M., Thorn complexes, Proc. London Math. Soc. 11 (1961), 291–310.Google Scholar
4. Feder, S. and Gitler, S., Stable homotopy Types of stunted complex projective spaces (to appear).Google Scholar
5. Held, R. P. and Sjerve, D., On the Spanier Conjecture, Comment. Math. Helv. 47 (1972), 75–91.Google Scholar
6. James, I., Spaces associated with Stiefel manifolds, Proc. London Math. Soc. 9 (1959), 115–140.Google Scholar
7. Quillen, D., The Adams Conjecture, Topology 10 (1971), 67–80.Google Scholar
8. Sigrist, F. and Suter, U., On symplectic Stiefel manifolds (to appear).Google Scholar
9. Toda, H., Composition methods in the homotopy groups of spheres, no. 49 (Princeton University Press, Princeton, N.J.).Google Scholar