The singular cohomology of the inverse limit of a Postnikov tower is representable
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- by Jerzy Dydak and Ross Geoghegan PDF
- Proc. Amer. Math. Soc. 98 (1986), 649-654 Request permission
Correction: Proc. Amer. Math. Soc. 103 (1988), 334.
Abstract:
Let ${X_1} \leftarrow {X_2} \leftarrow \cdots$ be an inverse sequence of spaces and maps satisfying (i) each ${X_n}$ has the homotopy type of a CW complex, (ii) each ${f_n}$ is a Hurewicz fibration, and (iii) the connectivity of the fiber of ${f_n}$ goes to $\infty$ with $n$. Let $\hat X$ be the inverse limit of the sequence. It is shown that the natural homomorphism $\check {H}^k(\hat {X},G) \to H^k(\hat {X}, G)$ (from Čech cohomology to singular cohomology, with ordinary coefficient module $G$) is an isomorphism for all $k$. It follows that ${\lim _{ \to n}}[{X_n},K(G,k)] \cong [\hat X,K(G,k)]$ for any Eilenberg- Mac Lane space $K(G,k)$. It is also shown that, except in trivial cases, $X$ does not have the homotopy type of a CW complex.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 649-654
- MSC: Primary 55S45; Secondary 54E60, 55P55
- DOI: https://doi.org/10.1090/S0002-9939-1986-0861769-8
- MathSciNet review: 861769