Volume 5, issue 1 (2005)

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Rational acyclic resolutions

Michael Levin

Algebraic & Geometric Topology 5 (2005) 219–235
 arXiv: math.GT/0410369
Abstract

Let $X$ be a compactum such that ${dim}_{ℚ}X\le n$, $n\ge 2$. We prove that there is a $ℚ$–acyclic resolution $r:\phantom{\rule{0.3em}{0ex}}Z\to X$ from a compactum $Z$ of $dim\le n$. This allows us to give a complete description of all the cases when for a compactum $X$ and an abelian group $G$ such that ${dim}_{G}X\le n$, $n\ge 2$ there is a $G$–acyclic resolution $r:\phantom{\rule{0.3em}{0ex}}Z\to X$ from a compactum $Z$ of $dim\le n$.

Keywords
cohomological dimension, acyclic resolution
Mathematical Subject Classification 2000
Primary: 55M10, 54F45