Classification theorems for cohomology rings of finite \(H\)-spaces
type: Item
instance of: scholarly article
title: Classification theorems for cohomology rings of finite \(H\)-spaces
zbMATH Open document ID: 1062.55006
author: Osamu Nishimura
published in: Journal of Mathematics of Kyoto University
publication date: 2004-12-29T00:00:00Z
review text: Let \(X\) be a simply-connected mod 3 finite \(H\)-space such that \(H_ \ast(X; {\mathbb F}_ 3)\) and \(K(2)_\ast(X)\) or \(K(3)_\ast(X)\) (where \(K(n)\) is the \(n\)-th periodic Morava \(K\)-theory at the prime 3) are associative. The author derives certain results on the relationship between the primitives and the indecomposables in the cohomology algebra \(H^\ast(X;{\mathbb F}_ 3)\). If \(K(2)_\ast(X)\) is associative, these results imply that \(H^\ast(X;{\mathbb F}_ 3)\) is isomorphic (as an algebra) to the mod~3 cohomology algebra of a finite product of the exceptional Lie groups \(F_ 4\), \(E_ 8\), and odd dimensional spheres different from \(S^ 1\).
reviewed by: Július Korbaš
Mathematics Subject Classification ID: 55P45
Mathematics Subject Classification ID: 55N20
zbMATH DE Number: 2124034
zbMATH Keywords: \(H\)-space
zbMATH Keywords: Hopf algebra
zbMATH Keywords: Morava \(K\)-theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250283746
OpenAlex ID: W1542791390
DOI: 10.1215/KJM/1250283746
description: scientific article; zbMATH DE number 2124034