#### Algebraic and Geometric Topology 3 (2003),
paper no. 46, pages 1277-1289.

## Cell-like resolutions preserving cohomological dimensions

### Michael Levin

**Abstract**.
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.
**Keywords**.
Cohomological dimension, cell-like resolution

**AMS subject classification**.
Primary: 55M10, 54F45.

**DOI:** 10.2140/agt.2003.3.1277

**E-print:** `arXiv:math.GN/0208148`

Submitted: 7 April 2003.
(Revised: 1 December 2003.)
Accepted: 9 December 2003.
Published: 31 December 2003.

Notes on file formats
Michael Levin

Department of Mathematics

Ben Gurion University of the Negev

P.O.B. 653

Be'er Sheva 84105, ISRAEL

Email: mlevine@math.bgu.ac.il

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