Closed model categories for uniquely \(S\)-divisible spaces
type: Item
instance of: scholarly article
title: Closed model categories for uniquely \(S\)-divisible spaces
zbMATH Open document ID: 1024.55007
DOI: 10.1016/S0022-4049(03)00016-1
published in: Journal of Pure and Applied Algebra
publication date: 2003-07-30T00:00:00Z
review text: For each integer \(n> 1\) and each multiplication system \(S\) of non-zero integers the authors define a new closed model category structure on the category of pointed spaces \(\text{Top}_*\). The weak equivalences are the maps that induce isomorphisms on the homotopy groups \(\pi_k(\mathbb{Z}[S^{-1}]; -)\) for \(k\geq n\). The corresponding localized category \(H_0(\text{Top}_*)\) is equivalent to the homotopy category of uniquely \((S,n)\)-divisible (i.e., \(\pi_k(-)\) is uniquely \(S\)-divisible for \(k\geq n\)) \((n-1)\)-connected spaces. When \(S= \mathbb{Z}\setminus\{0\}\), we recover the usual homotopy category of rational \(1\)-connected spaces.
reviewed by: Yves Félix
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 18D15
zbMATH DE Number: 1956709
zbMATH Keywords: uniquely \(S\)-divisible spaces
zbMATH Keywords: colocalization
zbMATH Keywords: closed model category
author: L. Javier Hernández
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1956709