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Equivariant self equivalences of principal fibre bundles

Published online by Cambridge University Press:  24 October 2008

Kouzou Tsukiyama
Affiliation:
Department of Mathematics, Shimane University, Matsue, Shimane, Japan and Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A.

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
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Federer, H.. A study of function spaces by spectral sequences. Trans. Amer. Math. Soc. 82 (1956), 340361.CrossRefGoogle Scholar
[2]Gottlieb, D. H.. Applications of bundle map theory. Trans. Amer. Math. Soc. 171 (1972), 2350.Google Scholar
[3]James, I. M.. The space of bundle maps. Topology 2 (1963), 4559.Google Scholar
[4]Lang, G. E.. The evaluation map and EHP sequence. Pacific J. Math. 44 (1973), 201210.CrossRefGoogle Scholar
[5]Matsuda, T.. On the n-equivariant self homotopy equivalences of spheres. J. Math. Soc. Japan 13 (1978), 4378.Google Scholar
[6]Matsuda, T.. On the equivariant self homotopy equivalences of spheres. J. Math. Soc. Japan 31 (1979), 6983.CrossRefGoogle Scholar
[7]Mimura, M. and Toda, H.. Homotopy groups of SU(3), SU(4) and Sp (2). J. Math. Kyoto Univ. 3 (1964), 217250.Google Scholar
[8]Mimura, M. and Toda, H.. Homotopy groups of symplectic groups. J. Math. Kyoto Univ. 3 (1964), 251273.Google Scholar
[9]Mimura, M.. The homotopy groups of Lie groups of low rank. J. Math. Kyoto Univ. 6 (1967), 131176.Google Scholar
[10]Schultz, R.. Homotopy decompositions of equivariant function spaces. Math. Z. 131 (1973), 4975.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), 103119.Google Scholar
[13]Tsukiyama, K.. On the group of fibre homotopy equivalences. Hiroshima Math. J. 12 (1982), 349376.Google Scholar
[14]Whitehead, G. W.. Elements of homotopy theory. Springer Graduate Texts in Math. 61 (1978).CrossRefGoogle Scholar