Abstract
Let B be a space which admits a numerable covering {U α :α ∈ Λ} with the property that every principal G-bundle over B is locally trivial with respect to the covering {U α }; let G(p) be the space of all equivariant automorphisms of p. In this setting the groups G(p) can be viewed as subgroups of some common group which depends only on the covering {U α } and G. We classify these groups G(p) up to conjugacy. In certain situations this leads to a characterization of the isomorphism classes of the groupsG(p).
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References
Booth, P., Heath,P., Morgan,C. and Piccinini, R.H-spaces of self-equivalences of fibrations and bundles, Proc.London Math.Soc.(3) 49 (1984), 111–127
Dold, A. -Halbexakte Homotopiefunktoren, Springer Lecture Notes in Mathematics 12, 1966
Hu, S. -The equivalence of fibre bundles, Annals of Math. 53 (1951), 256–275
Husemoller, D. -Fibre bundles, McGraw Hill Book Co., New York 1966
Koh,S.S. -Note on the homotopy properties of the components of the mapping space X s′, Proce.Amer.Math.Soc. 11 (1960), 896–904
May, J.P. -Classifying spaces and fibrations, Memoirs of the American Mathematical Society 155, Providence 1975
Steenrod, N. -The topology of fibre bundles, Princeton Univ. Press, Princeton 1951
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Morgan, C., Piccinini, R.A. Conjugacy classes of groups of bundle automorphisms. Manuscripta Math 63, 233–244 (1989). https://doi.org/10.1007/BF01168874
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DOI: https://doi.org/10.1007/BF01168874