Hurewicz isomorphism theorem for Steenrod homology

Abstract

For a pointed compactum (X, x), a natural homomorphism ξ n {\xi _n} from the Quigley’s approaching group π _ _ n ( X , x ) {\underline {\underline \pi } _n}(X,x) to the Steenrod homology group s H n + 1 ( X ) ^s{H_{n + 1}}(X) is defined. A shape theoretical condition under which ξ n {\xi _n} is an isomorphism is obtained. For every pointed S n {S^n} -like continuum (X, x), ξ n {\xi _n} is an isomorphism for n ≠ 2 n \ne 2 and ξ 2 {\xi _2} is an isomorphism if and only if X is movable.