Volume 3, issue 2 (2003)

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Cell-like resolutions preserving cohomological dimensions

Michael Levin

Algebraic & Geometric Topology 3 (2003) 1277–1289
 arXiv: math.GN/0208148
Abstract

We prove that for every compactum $X$ with ${dim}_{ℤ}X\le n\ge 2$ there is a cell-like resolution $r:Z\to X$ from a compactum $Z$ onto $X$ such that $dimZ\le n$ and for every integer $k$ and every abelian group $G$ such that ${dim}_{G}X\le k\ge 2$ we have ${dim}_{G}Z\le k$. The latter property implies that for every simply connected CW–complex $K$ such that $e-edimX\le K$ we also have $e-dimZ\le K$.

Keywords
Cohomological dimension, cell-like resolution
Mathematical Subject Classification 2000
Primary: 55M10, 54F45