\(H\)-spaces with Noetherian mod two cohomology algebra
type: Item
instance of: scholarly article
title: \(H\)-spaces with Noetherian mod two cohomology algebra
zbMATH Open document ID: 0927.55017
DOI: 10.1016/S0040-9383(98)00017-2
published in: Topology
publication date: 1999-12-13T00:00:00Z
review text: A subject of great interest is the classification of the mod 2 homotopy type of an \(H\)-space. A sub-family of this family is the set of the mod 2 finite \(H\)-space. The next larger one is the sub-family of the mod 2 \(H\)-spaces \(X\), where the cohomology ring \(H^*(X,F_2)\) is Noetherian. This paper classifies the mod 2 \(H\)-spaces with Noetherian mod 2 ring. This is done using the finite \(H\)-spaces, \((CP^\infty)^\wedge_2\), \(BZ/2^k\) and \(BZ/2^\infty\). The main results are too long to be stated here. But at least for the case where \(X\) is l-connected, the authors obtain: If \(X\) is l-connected mod 2 \(H\)-space with Noetherian mod 2 cohomology algebra, then there exists a mod 2 finite \(H\)-space \(F=F(X)\) and a principal \(H\)-fibration \(((CP^\infty)_2^\wedge)^n\to X\to F(X)\). The authors use extensively the techniques of Hopf algebras over the Steenrod algebra in spectral sequence, results of localization with respect to a map as developed by Dror, and the realization of certain algebraic maps as maps \(f:BV\to X\) where \(V\) is an elementary abelian group.
Mathematics Subject Classification ID: 55P45
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 55S10
zbMATH DE Number: 1307830
zbMATH Keywords: \(\text{mod} p H\)-spaces
zbMATH Keywords: Eilenberg-MacLane spaces
zbMATH Keywords: \(H\)-fibration
zbMATH Keywords: finite \(H\)-space
zbMATH Keywords: Steenrod algebra
author: Carles Broto
author: Juan A. Crespo
reviewed by: Daciberg Lima Gonçalves
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1307830