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Local to global properties in the theory of fibrations. (English) Zbl 0782.55006

Local to global theorems concerning the covering homotopy property, the weak covering homotopy property and the notion of fibre homotopy equivalence have been obtained by A. Dold in his fundamental paper [Ann. Math., II. Ser. 78, 223-255 (1963; Zbl 0203.254)].
In the present paper a systematic procedure for developing Dold-type results is given. Based on the notion of enriched spaces a technique is presented that via a fibred mapping space construction reduces questions in other theories to questions covered by Dold’s paper. Numerous applications including examples such as sectioned fibrations and principal \(G\)-fibrations are given.
Reviewer: K.H.Kamps (Hagen)

MSC:

55R05 Fiber spaces in algebraic topology

Citations:

Zbl 0203.254
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References:

[1] A.G. Allaud , On the classification of fiber spaces , Math Z. 92 ( 1966 ) 110 - 125 . MR 189035 | Zbl 0139.16603 · Zbl 0139.16603
[2] Bo1 P. Booth , Fibrations and cofibred pairs , Math. Scand. 35 ( 1974 ), 145 - 148 . Article | MR 370560 | Zbl 0302.55004 · Zbl 0302.55004
[3] Bo2 P. Booth , Fibrations and classifying spaces: an axiomatic approach , (to appear). Numdam | Zbl 0906.55010 · Zbl 0906.55010
[4] Br R. Brown , Topology , Ellis Horwood , Chichester , 1988 . MR 984598 | Zbl 0655.55001 · Zbl 0655.55001
[5] Do A. Dold , Partitions of unity in the theory of fibrations , Ann. of Math. 78 ( 1963 ), 223 - 255 . MR 155330 | Zbl 0203.25402 · Zbl 0203.25402
[6] E M.H. Eggar , The piecing comparison theorem , Nederl. Akad. Wetensch. Proc. Ser. A . 76 = Indag. Math. 35 ( 1973 ), 320 - 330 . MR 328925 | Zbl 0275.55015 · Zbl 0275.55015
[7] H D. Husemoller , Fibre Bundles , 2 nd edition, Springer-Verlag , Berlin , 1975 . MR 370578 | Zbl 0307.55015 · Zbl 0307.55015
[8] Ma J.P. May , Classifying spaces and fibrations , Memoirs Amer. Math. Soc. 155 ( 1975 ). MR 370579 | Zbl 0321.55033 · Zbl 0321.55033
[9] Mo1 C. Morgan , F-fibrations and groups of gauge transformations , Ph.D. thesis, Memorial University of Newfoundland , 1980 .
[10] Mo2 C. Morgan , Characterizations of F-fibrations , Proc. Amer. Math. Soc. 88 ( 1983 ), 169 - 172 . MR 691302 | Zbl 0542.55014 · Zbl 0542.55014
[11] Sp E. Spanier , Algebraic topology , McGraw-Hill , New York , 1966 . MR 210112 | Zbl 0145.43303 · Zbl 0145.43303
[12] St1 A. Strøm , Note on cofibrations , Math. Scand. 19 ( 1966 ), 11 - 14 . MR 211403 · Zbl 0145.43604
[13] St2 A. Strøm , Note on cofibrations II , Math. Scand. 22 ( 1968 ), 130 - 142 . MR 243525 | Zbl 0181.26504 · Zbl 0181.26504
[14] St3 A. Strøm , The homotopy category is a homotopy category , Arch. der Math. , 23 ( 1972 ), 435 - 441 . MR 321082 | Zbl 0261.18015 · Zbl 0261.18015
[15] V R.M. Vogt , Convenient categories of topological spaces for homotopy theory , Arch. Math. 22 ( 1971 ), 545 - 555 . MR 300277 | Zbl 0237.54001 · Zbl 0237.54001
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