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.

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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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