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We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n+1 and a surjective -map r: Z → X such that for every abelian group G and every integer k ≥ 2 such that we have and r is G-acyclic.
Michael Levin. "Universal acyclic resolutions for arbitrary coefficient groups." Fundamenta Mathematicae 178.2 (2003): 159-169. <http://eudml.org/doc/283189>.
@article{MichaelLevin2003, abstract = {We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n+1 and a surjective $UV^\{n-1\}$-map r: Z → X such that for every 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.}, author = {Michael Levin}, journal = {Fundamenta Mathematicae}, keywords = {cohomological dimension; -acyclic map; UV-map; covering dimension; acyclic resolution}, language = {eng}, number = {2}, pages = {159-169}, title = {Universal acyclic resolutions for arbitrary coefficient groups}, url = {http://eudml.org/doc/283189}, volume = {178}, year = {2003}, }
TY - JOUR AU - Michael Levin TI - Universal acyclic resolutions for arbitrary coefficient groups JO - Fundamenta Mathematicae PY - 2003 VL - 178 IS - 2 SP - 159 EP - 169 AB - We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n+1 and a surjective $UV^{n-1}$-map r: Z → X such that for every 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. LA - eng KW - cohomological dimension; -acyclic map; UV-map; covering dimension; acyclic resolution UR - http://eudml.org/doc/283189 ER -