Localization, completion and detecting equivariant maps on skeletons
type: Item
instance of: scholarly article
title: Localization, completion and detecting equivariant maps on skeletons
zbMATH Open document ID: 0698.55010
DOI: 10.1007/BF01168363
author: Nobuyuki Oda
author: Yoshimi Shitanda
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155422
review text: The authors extend results on phantom maps obtained by \textit{A. Zabrodsky} [Isr. J. Math. 58, 129-143 (1987; Zbl 0638.55020)] and the authors themselves [Publ. Res. Inst. Math. Sci. 24, 811-820 (1988; Zbl 0663.55006)] to results on so-called G-phantom maps in the category of equivariant spaces with base point. If f,g: \(X\to Y\) are two G-maps on a G-CW-complex, then f is called a G-phantom map when \(f/X^ n\) and \(g/X^ n\) are G-homotopic for all \(n\geq 0\). The authors give conditions under which G-maps induce injective maps between homotopy sets, and use this result, some consequences of it, and relations between the localization and the completion to characterize maps which are homotopic on skeletons.
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 55S37
Mathematics Subject Classification ID: 55S91
Mathematics Subject Classification ID: 55S35
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55P60
zbMATH DE Number: 4144941
zbMATH Keywords: G-Postnikov system
zbMATH Keywords: equivariant localization
zbMATH Keywords: equivariant completion
zbMATH Keywords: equivariant unstable homotopy spectral sequence
zbMATH Keywords: equivariant phantom maps
zbMATH Keywords: equivariant obstructions
zbMATH Keywords: equivariant spaces
zbMATH Keywords: G-maps
zbMATH Keywords: G-CW-complex
reviewed by: Götz Brunner
MaRDI profile type: Publication
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OpenAlex ID: W1995411464
description: scientific article; zbMATH DE number 4144941