On products of some \(\beta\)-elements in the homotopy of the \(\mod 3\) Moore spectrum
type: Item
instance of: scholarly article
title: On products of some \(\beta\)-elements in the homotopy of the \(\mod 3\) Moore spectrum
zbMATH Open document ID: 0899.55014
author: Yoshiko Arita
author: Katsumi Shimomura
published in: Hiroshima Mathematical Journal
publication date: 1998-02-11T00:00:00Z
review text: \textit{S. Pemmaraju}, in his still unpublished thesis, showed the existence of \(v_2\)-periodic elements \(\beta_s\) and \(\beta_s'\) in the 3-primary stable homotopy groups of the sphere and Moore spectrum \(M\) for \(s\equiv 0\), 1, 2, 5 or 6 mod 9. Under the assumption of Pemmaraju's results, the authors of this paper prove that certain products \(\beta_s' \beta_t\) and \(\beta_s' \beta_t'\) are nonzero in \(\pi_*M\), by using the results of their earlier paper [Hiroshima Math. J. 26, No. 2, 415-431 (1996; Zbl 0869.55010)] and by showing that these products are nonzero in the \(E_2\)-term of the Adams-Novikov spectral sequence.
Mathematics Subject Classification ID: 55Q10
Mathematics Subject Classification ID: 55Q52
Mathematics Subject Classification ID: 55T15
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 1117453
zbMATH Keywords: sphere spectrum
zbMATH Keywords: \(\beta\)-elements
zbMATH Keywords: homotopy groups
zbMATH Keywords: Moore spectrum
zbMATH Keywords: Adams-Novikov spectral sequence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206126965
OpenAlex ID: W1558566081
DOI: 10.32917/HMJ/1206126965
description: scientific article; zbMATH DE number 1117453