Universal acyclic resolutions for finitely generated coefficient groups

Details Universal acyclic resolutions for finitely generated coefficient groups Universal acyclic resolutions for finitely generated coefficient groups

2002-08-21

arxiv.org/abs/math/0208149v2

Topology Appl. 135(2004), 101--109

Mathematics

General Topology

Scientific paper

We prove that for every compactum X and every integer $n \geq 2$ there are a compactum Z of $\dim \leq n$ and a surjective $UV^{n-1}$-map $r: Z \lo X$ having the property that: for every finitely generated abelian group G and every integer $k \geq 2$ such that $\dim_G X \leq k \leq n$ we have $\dim_G Z \leq k$ and r is G-acyclic, or equivalently: for every simply connected CW-complex K with finitely generated homotopy groups such that $\edim X \leq K$ we have $\edim Z \leq K$ and r is K-acyclic. (A space is K-acyclic if every map from the space to K is null-homotopic. A map is K-acyclic if every fiber is K-acyclic.)

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