Algebraic and Geometric Topology 5 (2005), paper no. 12, pages 219-235.

Rational acyclic resolutions

Michael Levin

Abstract. Let X be a compactum such that dim_Q X <= n, n>1. We prove that there is a Q-acyclic resolution r: Z-->X from a compactum Z of dim <= n. This allows us to give a complete description of all the cases when for a compactum X and an abelian group G such that dim_G X <= n, n>1 there is a G-acyclic resolution r: Z-->X from a compactum Z of dim <= n.

Keywords. Cohomological dimension, acyclic resolution

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

DOI: 10.2140/agt.2005.5.219

E-print: arXiv:math.GT/0410369

Submitted: 17 March 2004. (Revised: 22 March 2005.) Accepted: 24 March 2005. Published: 6 April 2005.

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Michael Levin
Department of Mathematics, Ben Gurion University of the Negev
P.O.B. 653, Be'er Sheva 84105, ISRAEL

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