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Fibrations and classifying spaces: An axiomatic approach. I. (English) Zbl 0906.55010

L’auteur développe une théorie abstraite des fibrations, dans le but de donner des conditions générales sur une catégorie \({\mathcal E}\) d’espaces topologiques pour que, étant donné un espace \(F\) appartenant à \({\mathcal E}\), il existe une fibration universelle classant les fibrations de base un CW-complexe et de fibre \({\mathcal E}\)-homotopiquement équivalente à \(F\).
Reviewer: R.Cauty (Paris)

MSC:

55R10 Fiber bundles in algebraic topology
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References:

[1] B1 P.I. Booth , Local to global properties in the theory of fibrations , Cahiers de Topologie et Géométrie Différentielle Catégoriques , XXXIV - 2 ( 1993 ), 127 - 151 . Numdam | MR 1223656 | Zbl 0782.55006 · Zbl 0782.55006
[2] B2 P.I. Booth , Fibrations and classifying spaces: an axiomatic approach II (to appear , Cahiers de Topologie et Géométrie Différentielle Catégoriques ). Numdam | MR 1641846 | Zbl 0917.55009 · Zbl 0917.55009
[3] B3 P.I. Booth , Fibrations and classifying spaces: overview and examples (to appear) Numdam | Zbl 0991.55010 · Zbl 0991.55010
[4] B4 P.I. Booth , On the geometric bar construction and the Brown representability theorem (to appear, Cahiers de Topologie et Géométrie Différentielle Catégoriques ). Numdam | MR 1663342 | Zbl 0926.55011 · Zbl 0926.55011
[5] B(E) E.H. Brown , Abstract homotopy theory , Trans. Amer. Math. Soc. 119 ( 1965 ), 79 - 85 . MR 182970 | Zbl 0129.15301 · Zbl 0129.15301
[6] B(R) R. Brown , Topology: a geometric account of general topology, homotopy types and the fundamental groupoid , Ellis Horwood , Chichester , 1988 . MR 984598 | Zbl 0655.55001 · Zbl 0655.55001
[7] FP R. Fritsch and R.A. Piccinini , Cellular structures in topology , Cambridge University Press , Cambridge , 1990 . MR 1074175 | Zbl 0837.55001 · Zbl 0837.55001
[8] F.M. Fuchs , A note on mapping cylinders , Mich. Math. J. 18 , 289 - 290 ( 1971 ). Article | MR 287537 | Zbl 0224.55015 · Zbl 0224.55015
[9] M J.P. May , Classifying spaces and fibrations , Mem. Amer. Math. Soc. vol. 155 , Providence , 1975 . MR 370579 | Zbl 0321.55033 · Zbl 0321.55033
[10] V1 R.M. Vogt , Convenient categories of topological spaces for homotopy theory , Arch. Math XXII ( 1971 ), 545 - 555 . MR 300277 | Zbl 0237.54001 · Zbl 0237.54001
[11] V2 R.M. Vogt , A note on homotopy equivalences , Proc. Amer. Math. Soc. 32 ( 1972 ), 627 - 629 . MR 293632 | Zbl 0241.55009 · Zbl 0241.55009
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