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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The simplicial bundle of a CW fibration


Author: Donald W. Barnes
Journal: Proc. Amer. Math. Soc. 101 (1987), 559-562
MSC: Primary 55R05; Secondary 55R10, 55R20, 55T10
DOI: https://doi.org/10.1090/S0002-9939-1987-0908669-3
MathSciNet review: 908669
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Abstract: Suppose we are given a fibration $ p:E \to B$ over a connected base, with both base and fibre having the homotopy type of CW complexes. We construct a fibre bundle over $ B$ fibre homotopy equivalent to the given fibration and with fibre a simplicial complex. Further, the transformations of the fibre arising from the transition functions of this bundle are simplicial maps. From this, we deduce that the weak spectral sequence constructor axioms are sufficient to determine the Serre spectral sequence of a CW fibration.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0908669-3
Article copyright: © Copyright 1987 American Mathematical Society