Automorphisms of fibrations
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- by E. Dror, W. G. Dwyer and D. M. Kan PDF
- Proc. Amer. Math. Soc. 80 (1980), 491-494 Request permission
Abstract:
Let X be a simplicial set, G a simplicial group and $\bar WG$ the classifying complex of G. Then it is well known [1], [3] that the principal fibrations with base X and group G are classified by the components of the function complex ${(\bar WG)^X}$. The aim of the present note is to prove the following complement to this result (1.2): Let p be a principal fibration with base X and group G, and let aut p be its simplicial group of automorphisms (which keep the base fixed). Then $\bar W({\operatorname {aut}} p)$ has the homotopy type of the component of ${(\bar WG)^X}$ which (see above) corresponds to p. A similar result holds for ordinary fibrations.References
- M. G. Barratt, V. K. A. M. Gugenheim, and J. C. Moore, On semisimplicial fibre-bundles, Amer. J. Math. 81 (1959), 639–657. MR 111028, DOI 10.2307/2372920 E. Dror, W. G. Dwyer and D. M. Kan, Equivariant self homotopy equivalences, Proc. Amer. Math. Soc. (to appear).
- J. Peter May, Simplicial objects in algebraic topology, Van Nostrand Mathematical Studies, No. 11, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0222892
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 491-494
- MSC: Primary 55R15; Secondary 55U10
- DOI: https://doi.org/10.1090/S0002-9939-1980-0581012-1
- MathSciNet review: 581012