Equivariant weak \(n\)-equivalences
type: Item
instance of: scholarly article
title: Equivariant weak \(n\)-equivalences
zbMATH Open document ID: 0932.55010
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1999-03-14T00:00:00Z
full work available at URL: https://eudml.org/doc/120152
review text: This paper starts by giving a good account of the nonequivariant case together with a list of equivalent conditions for weak \(n\)-equivalences constructed by using homology with local coefficients. The main theorem in this paper provides a list of equivalent conditions for a map \(f:X\rightarrow Y\) between path connected CW-spaces to be a \(G\)-equivariant \(n\) equivalence where \(G\) is a discrete group and the fixed point spaces \(X^H\) and \(Y^H\) are path connected CW-spaces and satisfy that the groups \(\pi_1(X^H)\) and \(\pi_1(Y^H)\) are complete and the groups \(\Gamma_\pi\pi_k(Y^H,X^H)\) and \(\Gamma_\pi\pi_k(X^H)\) are trivial for \(k=2,\ldots,n\) and for every group \(H\subseteq G\).
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 55Q91
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 55P15
zbMATH DE Number: 1260646
zbMATH Keywords: \(G\)-CW-space
zbMATH Keywords: weak \(G\)-\(n\)-type
zbMATH Keywords: isotropy ring
zbMATH Keywords: Postnikov decomposition
zbMATH Keywords: universal covering
author: Marek Golasiński
author: Daciberg Lima Gonçalves
reviewed by: Juan Antonio Pérez
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1260646