Hostname: page-component-f554764f5-rj9fg Total loading time: 0 Render date: 2025-04-17T15:46:48.783Z Has data issue: false hasContentIssue false
  • English
  • Français

Equivariant self equivalences of principal fibre bundles

Published online by Cambridge University Press:  24 October 2008

Kouzou Tsukiyama
Kouzou Tsukiyama
Affiliation:
Department of Mathematics, Shimane University, Matsue, Shimane, Japan and Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

For a principal fibre bundle (p, q, B, G) with structure group G, the group of G-equivariant self equivalences of the total space P is investigated by using bundle map theory. Computations are given for well-known principal fibre bundles.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 1 , July 1985 , pp. 87 - 92
Copyright
Copyright © Cambridge Philosophical Society 1985

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Federer, H.. A study of function spaces by spectral sequences. Trans. Amer. Math. Soc. 82 (1956), 340–361.CrossRefGoogle Scholar
[2]Gottlieb, D. H.. Applications of bundle map theory. Trans. Amer. Math. Soc. 171 (1972), 23–50.Google Scholar
[3]James, I. M.. The space of bundle maps. Topology 2 (1963), 45–59.Google Scholar
[4]Lang, G. E.. The evaluation map and EHP sequence. Pacific J. Math. 44 (1973), 201–210.CrossRefGoogle Scholar
[5]Matsuda, T.. On the n-equivariant self homotopy equivalences of spheres. J. Math. Soc. Japan 13 (1978), 43–78.Google Scholar
[6]Matsuda, T.. On the equivariant self homotopy equivalences of spheres. J. Math. Soc. Japan 31 (1979), 69–83.CrossRefGoogle Scholar
[7]Mimura, M. and Toda, H.. Homotopy groups of SU(3), SU(4) and Sp (2). J. Math. Kyoto Univ. 3 (1964), 217–250.Google Scholar
[8]Mimura, M. and Toda, H.. Homotopy groups of symplectic groups. J. Math. Kyoto Univ. 3 (1964), 251–273.Google Scholar
[9]Mimura, M.. The homotopy groups of Lie groups of low rank. J. Math. Kyoto Univ. 6 (1967), 131–176.Google Scholar
[10]Schultz, R.. Homotopy decompositions of equivariant function spaces. Math. Z. 131 (1973), 49–75.Google Scholar
[11]Steenrod, N. E.. The topology of fibre bundles (Princeton University Press, 1951).CrossRefGoogle Scholar
[12]Toda, H.. A topological proof of theorems of Bott and Borel-Hirzebruch for homotopy groups of unitary groups. Mem. Col. Sci. Univ. of Kyoto. 32 (1959), 103–119.Google Scholar
[13]Tsukiyama, K.. On the group of fibre homotopy equivalences. Hiroshima Math. J. 12 (1982), 349–376.Google Scholar
[14]Whitehead, G. W.. Elements of homotopy theory. Springer Graduate Texts in Math. 61 (1978).CrossRefGoogle Scholar