The vanishing of Steenrod squares on H-spaces
type: Item
instance of: scholarly article
title: The vanishing of Steenrod squares on H-spaces
zbMATH Open document ID: 0661.55015
DOI: 10.1007/BF02566751
author: James P. Lin
published in: Commentarii Mathematici Helvetici
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140107
review text: Let X be a simply connected finite H-space whose mod 2 homology is an associative ring. The author shows that for \(r\geq 0\) and \(k>0\) \[ QH^{2^ r+2^{r+1}k-1}(X)\subseteq Sq^{2^ r}H^*(\Omega X) \] and \[ Sq^{2^ r}QH^{2^ r+2^{r+1}k-1}(X)=0 \] and concludes that many Steenrod operations take indecomposables to decomposables. The primitively generated case of this result was proved by \textit{E. Thomas} [Ann. Math., II. Ser. 77, 306-317 (1963; Zbl 0115.403) and ibid. 81, 473-495 (1965; Zbl 0127.135)].
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 55P45
Mathematics Subject Classification ID: 55R35
zbMATH DE Number: 4080414
zbMATH Keywords: Hopf structure
zbMATH Keywords: simply connected finite H-space
zbMATH Keywords: Steenrod operations
zbMATH Keywords: indecomposables
reviewed by: Marek Golasiński
MaRDI profile type: Publication
OpenAlex ID: W2038626231
description: scientific article; zbMATH DE number 4080414