Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T19:37:35.552Z Has data issue: false hasContentIssue false
  • English
  • Français

Hypersurfaces Framées et L'Élément β1, de Toda

Published online by Cambridge University Press:  20 November 2018

A. Baker ,
N. Ray  and
L. Schwartz
A. Baker
Affiliation:
Department of Mathematics, the University Manchester, M139PL, Great-Britain
N. Ray
Affiliation:
Department of Mathematics, the University Manchester, M139PL, Great-Britain
L. Schwartz
Affiliation:
UA 1169 DU C.N.R.S. Université Paris XI, Bâtiment 425 91405 Orsay Cedex, France
Rights & Permissions [Opens in a new window]

Résumé

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.

L'objet de cet article est de construire un modèle pour l'élément β1, de Toda (premier élément non nul de la composante p - primaire de l'homotopie stable des sphères qui n'est pas dans l'image du J-homomorphisme, p ≠ 2). Le modèle construit possède en outre la propriété de se plonger, comme variété différentiable, en codimension 1.

La construction, basée sur la J-théorie et la chirurgie, exhibe en outre des complexes cellulaires satisfaisant à certaines conditions de plongement, répondant partiellement à un problème posé par le 2e et le 3e auteur.

Keywords

primary 57R15Secondary 55Q45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 215 - 222
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Atiyah, M. et Smith, L., Compact Lie groups and the stable homotopy of spheres, Topology 13 (1974), 135–142.Google Scholar
2. Browder, W., Surgery on simply connected manifolds, Springer-Verlag, 1972.Google Scholar
3. Carlisle, D., Eccles, P., Hilditch, S., Ray, N., Schwartz, L., Walker, G. et Wood, R., Modular representations ofGL(n, p), splitting (∑(Cℙ∞ x ••• x Cℙ∞) and the β-family as framed surfaces, Math. Z. 189 (1985), 239–261.Google Scholar
4. Franjou, V. et Schwartz, L., Hypersurfaces et homotopie stable de U, Notes aux C.R.A.S. Paris, t. 299, série I, n° 13 (1984).Google Scholar
5. Hirsch, M. et Mazur, B., Smoothings of PL-manifolds, Annals of Math. Studies , Princeton U. Press, 1980.Google Scholar
6. Knapp, K.H., Some applications of K-theory to framed bordism, e-invariant and transfert, Habilitations-schrift , Bonn (1979).Google Scholar
7. Kobayashi, T., Maki, H., Nakamura, O. et Umehara, J., Some non embedding theorems up to homotopy type, Memoir Fac. Soc. Kochi Univ., série A, Math. vol. 3 (1982).Google Scholar
8. Ray, N., Framed manifolds for the element β1 , Indiana Univ. Math. Journal (28) n° 2 (1979).Google Scholar
9. Ray, N. et Schwartz, L., Embedding certain complexes via unstable homotopy theory, AMS Contemp. Math. 19(1983).Google Scholar
10. Rees, E., Framing on hypersurfaces, J. London Math. Soc. 22 (1980).Google Scholar
11. Rourke, C. et Sullivan, D., On the Kervaire obstruction, Ann. of Math. 94 (1971).Google Scholar
12. Sullivan, D., Genetics ofhomotopy theory and the Adams conjecture, Ann. of Math. n° 100 (1974), 1–79.Google Scholar
13. Wall, C. T.C., Surgery on compact manifolds, Academic Press (1970).Google Scholar