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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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