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Universal acyclic resolutions for arbitrary coefficient groups

Abstract

We prove that for every compactum XX and every integer n2n \geq 2 there are a compactum ZZ of dimn+1\dim \leq n+1 and a surjective UVn1UV^{n-1}-map r: Z \lo X such that for every abelian group GG and every integer k2k \geq 2 such that dimGXkn\dim_G X \leq k \leq n we have dimGZk\dim_G Z \leq k and rr is GG-acyclic

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