Universal acyclic resolutions for finitely generated coefficient groups

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We prove that for every compactum X and every integer n≥2 there are a compactum Z of dim≤n and a surjective UVn-1-map r :Z→X having the property that: for every finitely generated Abelian group G and every integer k≥2 such that dimGX≤k≤n we have dimGZ≤k and r is G-acyclic, or equivalently: for every simply connected CW-complex K with finitely generated homotopy groups such that e-dimX≤K we have e-dimZ≤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.)

Original languageEnglish
Pages (from-to)101-109
Number of pages9
JournalTopology and its Applications
Issue number1-3
StatePublished - 1 Jan 2004


  • Cell-like and acyclic resolutions
  • Cohomological dimension

ASJC Scopus subject areas

  • Geometry and Topology


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