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Hurewicz isomorphism theorem for Steenrod homology


Authors: Y. Kodama and A. Koyama
Journal: Proc. Amer. Math. Soc. 74 (1979), 363-367
MSC: Primary 55N07; Secondary 54F43, 55Q07, 55Q99
DOI: https://doi.org/10.1090/S0002-9939-1979-0524318-6
MathSciNet review: 524318
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Abstract: For a pointed compactum (X, x), a natural homomorphism $ {\xi _n}$ from the Quigley's approaching group $ {\underline{\underline \pi } _n}(X,x)$ to the Steenrod homology group $ ^s{H_{n + 1}}(X)$ is defined. A shape theoretical condition under which $ {\xi _n}$ is an isomorphism is obtained. For every pointed $ {S^n}$-like continuum (X, x), $ {\xi _n}$ is an isomorphism for $ n \ne 2$ and $ {\xi _2}$ is an isomorphism if and only if X is movable.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0524318-6
Keywords: Shape, movability, Steenrod homology, Hurewicz isomorphism theorem
Article copyright: © Copyright 1979 American Mathematical Society

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