Rational acyclic resolutions

Levin, Michael

doi:10.2140/agt.2005.5.219

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Rational acyclic resolutions

Michael Levin

Algebraic & Geometric Topology 5 (2005) 219–235

DOI: 10.2140/agt.2005.5.219

arXiv: math.GT/0410369

Abstract

Let $X$ be a compactum such that ${dim}_{ℚ} X \leq n$ , $n \geq 2$ . We prove that there is a $ℚ$ –acyclic resolution $r : Z \to X$ from a compactum $Z$ of $dim \leq n$ . This allows us to give a complete description of all the cases when for a compactum $X$ and an abelian group $G$ such that ${dim}_{G} X \leq n$ , $n \geq 2$ there is a $G$ –acyclic resolution $r : Z \to X$ from a compactum $Z$ of $dim \leq n$ .

Keywords

cohomological dimension, acyclic resolution

Mathematical Subject Classification 2000

Primary: 55M10, 54F45

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Publication

Received: 17 March 2004

Revised: 22 March 2005

Accepted: 24 March 2005

Published: 6 April 2005

Authors

Michael Levin
Department of Mathematics Ben Gurion University of the Negev P.O.B. 653 Be’er Sheva 84105 Israel

Volume 5, issue 1 (2005)