Fibrations over a CWh-base
Author:
Rolf Schön
Journal:
Proc. Amer. Math. Soc. 62 (1977), 165-166
MSC:
Primary 55F05
DOI:
https://doi.org/10.1090/S0002-9939-1977-0431163-7
MathSciNet review:
0431163
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Abstract | References | Similar Articles | Additional Information
Abstract: This note provides a short argument for the known fact that the total space of a fibration has the homotopy type of a CW-complex if base and fiber have.
- G. Allaud, De-looping homotopy equivalences, Arch. Math. (Basel) 23 (1972), 167–169. MR 309106, DOI https://doi.org/10.1007/BF01304862
- Rita Ciampi and Giuseppe De Cecco, Gruppi d’omotopia di Čech, An. Univ. Bucureşti Mat.-Mec. 22 (1973), no. 2, 87–101 (Italian, with French summary). MR 362297
- Albrecht Dold, Partitions of unity in the theory of fibrations, Ann. of Math. (2) 78 (1963), 223–255. MR 155330, DOI https://doi.org/10.2307/1970341
- Ronald Brown and Philip R. Heath, Coglueing homotopy equivalences, Math. Z. 113 (1970), 313–325. MR 266213, DOI https://doi.org/10.1007/BF01110331
- Klaus Heiner Kamps, Kan-Bedingungen und abstrakte Homotopiethoerie, Math. Z. 124 (1972), 215–236 (German). MR 295346, DOI https://doi.org/10.1007/BF01110801
- John Milnor, On spaces having the homotopy type of a ${\rm CW}$-complex, Trans. Amer. Math. Soc. 90 (1959), 272–280. MR 100267, DOI https://doi.org/10.1090/S0002-9947-1959-0100267-4
- J. Peter May, Classifying spaces and fibrations, Mem. Amer. Math. Soc. 1 (1975), no. 1, 155, xiii+98. MR 370579, DOI https://doi.org/10.1090/memo/0155
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
- James Stasheff, A classification theorem for fibre spaces, Topology 2 (1963), 239–246. MR 154286, DOI https://doi.org/10.1016/0040-9383%2863%2990006-5
- Robert M. Switzer, Algebraic topology—homotopy and homology, Springer-Verlag, New York-Heidelberg, 1975. Die Grundlehren der mathematischen Wissenschaften, Band 212. MR 0385836
- J. H. C. Whitehead, A certain exact sequence, Ann. of Math. (2) 52 (1950), 51–110. MR 35997, DOI https://doi.org/10.2307/1969511
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Article copyright:
© Copyright 1977
American Mathematical Society