Abstract
For a general fibration of connected spaces F → E → B, the map R∞E → R∞B is always a fibration (Ch.I, 4.2), but R∞F need not have the same homotopy type as the fibre of R∞E → R∞B. For example, if R = Q, then
is, up to homotopy, a fibration, but R∞S2 → R∞P2 → R∞K(Z2,1) is not, because (Ch.I, 5.5) R∞P2 and R∞K(Z2,1) are contractible, while R∞S2 is not.
Keywords
- Exact Sequence
- Spectral Sequence
- Short Exact Sequence
- Homotopy Type
- Connected Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 1972 Springer-Verlag Berlin Heidelberg
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Bousfield, A.K., Kan, D.M. (1972). Fibre lemmas. In: Homotopy Limits, Completions and Localizations. Lecture Notes in Mathematics, vol 304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38117-4_2
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DOI: https://doi.org/10.1007/978-3-540-38117-4_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06105-2
Online ISBN: 978-3-540-38117-4
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