Localization of homotopy epimorphisms and homotopy monomorphisms
type: Item
instance of: scholarly article
title: Localization of homotopy epimorphisms and homotopy monomorphisms
zbMATH Open document ID: 0852.55018
author: Zaisi Zuo
author: Wenhuai Shen
published in: Chinese Science Bulletin
publication date: 1996-12-08T00:00:00Z
review text: Let \(f : X \to Y\) be a map between pointed connected CW-complexes and \(f_p : X_p \to Y_p\) be its \(p\)-localization, where \(p\) is either a prime or 0. It is shown that if \(X_p\) and \(Y_p\) are nilpotent and \(f\) is a homotopy epimorphism (monomorphism which is \(\text{mod } p\) nilpotent), then \(f_p\) is a homotopy epimorphism (monomorphism). For \(p = 3\), an example is constructed of a homotopy monomorphism \(f : X \to Y\) such that \(X_p\) and \(Y_p\) are nilpotent but \(f_p\) is not a homotopy monomorphism.
Mathematics Subject Classification ID: 55P60
zbMATH DE Number: 817787
zbMATH Keywords: localization
zbMATH Keywords: nilpotent
zbMATH Keywords: homotopy epimorphism
zbMATH Keywords: homotopy monomorphism
reviewed by: Zbigniew Karno
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 817787