Homology, Homotopy and Applications
Volume 12 (2010)
Generalized Steenrod homology theories are strong shape invariant
Pages: 1 – 23
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.
Steenrod homology theory; pointed strong shape theory; strong excision axiom; cone collapsing axiom; quotient exactness axiom
2010 Mathematics Subject Classification
55N20, 55N40, 55P55