Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-24T01:11:48.448Z Has data issue: false hasContentIssue false
  • English
  • Français

On conjectures of Mahowald, Segal and Sullivan

Published online by Cambridge University Press:  24 October 2008

Wen-Hsiung Lin
Wen-Hsiung Lin
Affiliation:
National Cheng-Chi University, Taipei, Taiwan
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we prove some results about the stable homotopy and cohomotopy of spaces related to the infinite real protective space RP∞. These include M. E. Mahowald's conjecture on the limit of stable homotopy of stunted real projective spaces RP2N+m/RP2N−m as N, m → ∞, G. Segal's Burnside ring conjecture for

and the stable analogue of a conjecture of D. Sullivan on RP∞.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 3 , May 1980 , pp. 449 - 458
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)Adams, J. F.On the structure and applications of the Steenrod algebra. Comm. Math. Helv. 32 (1958), 180–214.CrossRefGoogle Scholar
(2)Adams, J. F.Vector fields on spheres. Ann. of Math. 75 (1962), 603–632.CrossRefGoogle Scholar
(3)Adams, J. F.Stable homotopy and generalized homology (University of Chicago Press, 1974).Google Scholar
(4)Adams, J. F. Operations of the nth kind in K-theory and what we don't know about RP∞. London Math. Soc. Lect. Notes Series 11 (Cambridge University Press, 1974, pp. 1–9).Google Scholar
(5)Adams, J. F.Graeme Segal's Burnside ring conjecture To appear in the Proceedings of a conference in Siegen,Federal Republic of Germany.Google Scholar
(6)Atiyah, M. F.Thom complexes. Proc. London Math. Soc. (3) 11 (1961), 291–310.CrossRefGoogle Scholar
(7)James, I. M. The topology of Stiefel manifolds. London Math. Soc. Lect. Notes Series, 24 (Cambridge University Press, 1976).Google Scholar
(8)Laitinen, E.On the Burnside ring and stable cohomotopy of a finite group (Aarhus University Publication, 1978).Google Scholar
(9)Lin, W. H.The Adams–Mahowald conjecture on real projective spaces. Math. Proc. Cambridge Philos. Soc. (to appear).Google Scholar
(10)Lin, W. H., Davis, D. M., Mahowald, M. E. & Adams, J. F.Calculation of Lin's Ext groups. Math. Proc. Cambridge Philos. Soc. 87 (1980), 459–469.CrossRefGoogle Scholar
(11)Mahowald, M. E.The metastable homotopy of Sn. Mem. Amer. Math. Soc. no. 72 (s.967).Google Scholar
(12)Mahowald, M. E. Some homotopy classes generated by ηj. Proc. of Aarhus Conference, 1978 (to appear in Springer-Verlag Lecture Notes Series).Google Scholar
(13)Sullivan, D.Geometric Topology, I. Localization, Periodicity and Galois Symmetry (M.I.T. mimeograph notes, 1970).Google Scholar