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The simplicial bundle of a CW fibration. (English) Zbl 0663.55010

This note extends results from the author’s “Spectral sequence constructors in algebra and topology” [Mem. Am. Math. Soc. 53 (1985; Zbl 0557.18006)]. In the earlier work, constructions held for simplicial bundles and, in this paper, they are extended to CW-fibrations. In particular, if p: \(E\to B\) is a fibration with B and fibres \(p^{-1}(b)\) have the homotopy type of CW-complexes, then any two spectral sequence constructors, F and \(F'\); applied to p yield the same spectral sequence. The method of proof follows Milnor’s construction of universal bundles.
Reviewer: J.McCleary

MSC:

55T10 Serre spectral sequences
55R20 Spectral sequences and homology of fiber spaces in algebraic topology
55R05 Fiber spaces in algebraic topology

Citations:

Zbl 0557.18006
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References:

[1] D. W. Barnes, Spectral sequence constructors in algebra and topology, Mem. Amer. Math. Soc. 53 (1985), no. 317, viii+174. · Zbl 0557.18006 · doi:10.1090/memo/0317
[2] Edward Fadell, On fiber homotopy equivalence, Duke Math. J 26 (1959), 699 – 706. · Zbl 0105.35301
[3] Edward Fadell, The equivalence of fiber spaces and bundles, Bull. Amer. Math. Soc. 66 (1960), 50 – 53. · Zbl 0104.39703
[4] John Milnor, Construction of universal bundles. I, Ann. of Math. (2) 63 (1956), 272 – 284. · Zbl 0071.17302 · doi:10.2307/1969609
[5] N. E. Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967), 133 – 152. · Zbl 0145.43002
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