Generalized Steenrod homology theories are strong shape invariant

It is shown that a reduced homology theory on the category of pointed compact metric spaces is strong shape invariant if and only if its homology functors $h_n$ satisfy the quotient exactness axiom, which means that for each pointed compact metric pair $(X, A, a_0)$ the natural sequence $h_n(A, a_0) \to h_n(X, a_0) \to h_n(X/A, *)$ is exact. As a consequence, all generalized Steenrod homology theories are strong shape invariant.

Keywords

Steenrod homology theory, pointed strong shape theory, strong excision axiom, cone collapsing axiom, quotient exactness axiom

2010 Mathematics Subject Classification

55N20, 55N40, 55P55

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Published 1 January 2010