Universal acyclic resolutions for finitely generated coefficient groups

2002/08/31 by Michael Levin
Mathematics · #math.GN #math.AT #msc:55M10 #msc:54F45

paper · pdf

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

arxiv created 2004/01/13 · arxiv updated 2009/11/30

Abstract

We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dim ≤ 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 ≥ 2 such that dim_G X ≤ k ≤ n we have dim_G Z ≤ k and r is G-acyclic, or equivalently: for every simply connected CW-complex K with finitely generated homotopy groups such that \edim X ≤ K we have \edim Z ≤ 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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• Acyclic resolutions for arbitrary groups
• Simultaneous Z/p-acyclic resolutions of expanding sequences
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