Universal acyclic resolutions for arbitrary coefficient groups

Michael Levin¹

¹ Department 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 $n\ge 2$ there are a compactum $Z$ of dimension $\le n+1$ and a surjective $U{V}^{n-1}$-map $r:Z\to X$ such that for every abelian group $G$ and every integer $k\ge 2$ such that ${\dim }_{G}X\le k\le n$ we have ${\dim }_{G}Z\le k$ and $r$ is $G$-acyclic.

Détail

DOI : 10.4064/fm178-2-5

Mots-clés : 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