The structure of the Hurewicz homomorphism
type: Item
instance of: scholarly article
zbMATH Open document ID: 0986.55011
author: Christopher Schwartz
author: Donald W. Kahn
publication date: 2002-06-06T00:00:00Z
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55S45
Mathematics Subject Classification ID: 55P99
Mathematics Subject Classification ID: 55N99
zbMATH DE Number: 1639904
zbMATH Keywords: Postnikov tower
zbMATH Keywords: Moore spaces
zbMATH Keywords: split monomorphism
zbMATH Keywords: split epimorphism
MaRDI profile type: Publication
title: The structure of the Hurewicz homomorphism
review text: The authors study the Hurewicz homomorphism from the viewpoint of the spectral sequence of a Postnikov tower and work in the category of pointed spaces which have the homotopy type of a simple connected (or simple) based CW-complex with locally-finite homology. In order to illustrate results obtained in the paper let us ask ourselves when the Hurewicz homomorphism \(h_n: \pi_n(X) \to H_n(X)\) is an isomorphism in all dimensions? Then the answer is the following statement: The only simple, noncontractible space, for which \(h_n\) is an isomorphism in all dimensions is the circle \(S^1\). Analogous questions are studied when the Hurewicz homomorphism is monomorphism, split monomorphism, epimorphism, and split epimorphism.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00050].
reviewed by: Ivan Ivanšić
description: scientific article; zbMATH DE number 1639904