Cell-like resolutions preserving cohomological dimensions

Details Cell-like resolutions preserving cohomological dimensions Cell-like resolutions preserving cohomological dimensions

2002-08-21

arxiv.org/abs/math/0208148v2

Algebr. Geom. Topol. 3 (2003) 1277-1289

Mathematics

General Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-46.abs.html

Scientific paper

We prove that for every compactum X with dim_Z X <= n >= 2 there is a
cell-like resolution r: Z --> X from a compactum Z onto X such that dim Z <= n
and for every integer k and every abelian group G such that dim_G X <= k >= 2
we have dim_G Z <=k. The latter property implies that for every simply
connected CW-complex K such that e-dim X <= K we also have e-dim Z <= K.

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