The homotopy fiber of profinite completion
type: Item
instance of: scholarly article
title: The homotopy fiber of profinite completion
zbMATH Open document ID: 0957.55009
DOI: 10.1016/S0166-8641(99)00006-1
author: Joseph Roitberg
author: Pat Touhey
published in: Topology and its Applications
publication date: 2001-03-29T00:00:00Z
review text: For \(Y\) a nilpotent space of finite type with finite fundamental group and Sullivan's profinite completion map \(c:Y\to \widehat{Y}\), the authors show that the basepoint-component of the homotopy fiber of \(c\) is always an \(H\)-space. This observation allows for a reworking of the completion/rationalization approach to phantom map theory. Under this hypothesis and for any connected CW-complex \(X\), they prove \[ Ph(X,Y)\approx \frac{\prod_{n\geq 1}H^n (X; \pi_{n+1} Y\otimes \widehat{Z}/Z)} {[X, \Omega\widehat{Y}]}. \] Using this, they obtain more direct, transparent proofs of various results from the present literature on phantom maps.
reviewed by: Corina Mohorianu
Mathematics Subject Classification ID: 55P60
zbMATH DE Number: 1454828
zbMATH Keywords: rationalization
zbMATH Keywords: phantom map
MaRDI profile type: Publication
full work available at URL: s0166-8641(99)00006-1
OpenAlex ID: W2094824715
description: scientific article; zbMATH DE number 1454828