The convergence of \(\tilde\alpha_s^{(n)}h_0h_k\)
type: Item
instance of: scholarly article
title: The convergence of \(\tilde\alpha_s^{(n)}h_0h_k\)
zbMATH Open document ID: 0947.55015
DOI: 10.1007/BF02876232
published in: Science in China. Series A
publication date: 1999-10-25T00:00:00Z
review text: The authors show that the following elements are nonbounding infinite cycles in the classical mod \(p\) Adams spectral sequence for \(\pi_*^S\): (1) \(\widetilde\beta_s h_0h_{k+1}\) for \(p\geq 5\) prime, \(2\leq s\leq p-1\), \(k\geq 2\); (2) \(\widetilde\gamma_s h_0h_{k+1}\) for \(p\geq 7\) prime, \(3\leq s\leq p-1\), \(k\geq 3\). Their proof uses the existence of maps \(v_n: \Sigma^{2(p^n-1)} V(n-1)\to V(n-1)\), the convergence of the \(h_0b_k\) to elements \(\zeta_k\) [\textit{R. L. Cohen}, Odd primary infinite families in stable homotopy theory, Mem. Am. Math. Soc. 242 (1981; Zbl 0452.55009)] and computations in the cobar construction.
Mathematics Subject Classification ID: 55Q45
Mathematics Subject Classification ID: 55T15
zbMATH DE Number: 1329978
zbMATH Keywords: stable stems
zbMATH Keywords: Adams spectral sequence
zbMATH Keywords: cobar construction
author: Xiangjun Wang
author: Qi-Bing Zheng
reviewed by: Stanley O. Kochman
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02876232
OpenAlex ID: W2091498518
description: scientific article; zbMATH DE number 1329978