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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 dimX n 2 there is a cell-like resolution r : ZX from a compactum Z onto X such that dimZ n and for every integer k and every abelian group G such that dimGX k 2 we have dimGZ k. The latter property implies that for every simply connected CW–complex K such that e-edimX K we also have e-dimZ K.

Keywords
Cohomological dimension, cell-like resolution
Mathematical Subject Classification 2000
Primary: 55M10, 54F45
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Publication
Received: 7 April 2003
Revised: 1 December 2003
Accepted: 9 December 2003
Published: 31 December 2003
Authors
Michael Levin
Department of Mathematics
Ben Gurion University of the Negev
P.O.B. 653
Be’er Sheva 84105
ISRAEL