Universal acyclic resolutions for arbitrary coefficient groups

Michael Levin¹

¹Department of Mathematics Ben Gurion University of the Negev P.O. Box 653 Be'er Sheva 84105, Israel

Fundamenta Mathematicae, Tome 178 (2003) no. 2, pp. 159-169

Résumé

We prove that for every compactum $X$ and every integer $n \geq 2$ there are a compactum $Z$ of dimension $\leq n+1$ and a surjective $UV^{n-1}$-map $r: Z \to X$ such that for every abelian group $G$ and every integer $k \geq 2$ such that $\mathop {\rm dim}\nolimits _G X \leq k \leq n$ we have $\mathop {\rm dim}\nolimits _G Z \leq k$ and $r$ is $G$-acyclic.

Détail

DOI : 10.4064/fm178-2-5

Keywords: prove every compactum every integer geq there compactum dimension leq surjective n map every abelian group every integer geq mathop dim nolimits leq leq have mathop dim nolimits leq g acyclic