Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T23:55:07.105Z Has data issue: false hasContentIssue false
  • English
  • Français

Characteristic Classes for Spherical Fiber Spaces

Published online by Cambridge University Press:  22 January 2016

Akihiro Tsuchiya
Akihiro Tsuchiya*
Affiliation:
Mathematical Institute, Nagoya University
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 SF = SG denote the space , and BSF be the classifying space of SF. Our purpose is to determine H*(BSF: Zp) as a Hopf algebra over Zp where p is an odd prime number. We have announced the main result in [14].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 43 , September 1971 , pp. 1 - 39
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Adem, J., The Relations on Steenrod Reduced Powers of Cohomology Classes. Algebraic geometry and Topology. Princeton.Google Scholar
[2] Araki, S. and Kudo, , Topology of H n-spaces and H-squring operations, Memories of the Faculty of Science, Kyushu Univ. 10. 85–120 (1956).Google Scholar
[3] Browder, W., On differentiable Hopf algebras. Transaction of the Amer. Math. 153–176 (1963).CrossRefGoogle Scholar
[4] Dyer, E. and Lashof, R.K., Homology of iterated loop spaces, Amer. J. Math. 84. 35–88 (1962).CrossRefGoogle Scholar
[5] Hall, I.M., The generalized Whitney sum. Quart. J. Math. 16. 360–384 (1965).CrossRefGoogle Scholar
[6] Kambe, T., The structure of KΛ-rings of the lens spaces and their Applications. Jour. Math. Soc. of Japan, 18. 135–146 (1966).Google Scholar
[7] P-May, The homology of F, F/0, BF, preprint.Google Scholar
[8] Milnor, J., On characteristic classes for spherical fiber spaces, Comment. Math. Helv. 43. 51–77 (1968).CrossRefGoogle Scholar
[9] Milnor, J. and Moore, J.C., On the structure of Hopf algebras, Ann. of Math. 81. 211–264 (1965).CrossRefGoogle Scholar
[10] Nakaoka, M., Cohomology theory of a complex with a transformation of prime period and its applications, Jour, of the Inst. Poly. Osaka City Univ. 7. 52–101 (1956).Google Scholar
[11] Nishida, G., Cohomology Operations in iterated loop spaces, Proc. of the Japan acad. 44, No. 3. 104–109 (1968).Google Scholar
[12] Peterson, F.K. and Toda, H., On the structure H*(BSF:Zp) Jour, of Math, of Kyoto Univ. Vol. 7. No. 2. 113–121 (1967).Google Scholar
[13] Steenrod, N.E., Cohomology operations. Ann. Math. Study. 51. (1962).Google Scholar
[14] Tsuchiya, A., Characteristic classes for spherical fiber spaces, Proc. of the Japan acad., 44. No. 7, 617–622 (1968).Google Scholar
[15] Tsuchiya, A., Characteristic classes for P.L.-micro bundles, Nagoya Math. Journal. Vol 43.Google Scholar