\(H\)-spaces with Noetherian mod two cohomology algebra
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.
scientific article; zbMATH DE number 1307830