Hurewicz isomorphism theorem for Steenrod homology

Kodama, Y.; Koyama, A.

doi:10.1090/S0002-9939-1979-0524318-6

Hurewicz isomorphism theorem for Steenrod homology
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by Y. Kodama and A. Koyama PDF

Proc. Amer. Math. Soc. 74 (1979), 363-367 Request permission

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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