The transfer and James-Hopf invariants
type: Item
instance of: scholarly article
title: The transfer and James-Hopf invariants
zbMATH Open document ID: 0609.55006
DOI: 10.1007/BF01200360
author: Nicholas J. Kuhn
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173890
review text: If X is a connected space, there is an equivalence \(\Sigma ^{\infty}QX=\bigvee _{q\geq 1}\Sigma ^{\infty}D_ qX\) arising from Hopf invariants \(j_ q: QX\to QD_ qX\), where \(QX=\Omega ^{\infty}\Sigma ^{\infty}X\) and \(D_ qX=E \Sigma _{q+} \bigwedge _{\Sigma _ q} X^{[q]}\). Let \(f^ n_{r,q}\) be the composite \[ \Sigma ^{\infty}D_ nX\quad \to \quad \Sigma ^{\infty}QX\quad \to ^{\Sigma ^{\infty}j_ q}\quad \Sigma ^{\infty}QD_ qX\quad \to \quad \Sigma ^{\infty}D_ rD_ qX\quad. \] We describe \(f^ n_{r,q}\) in terms of more familiar maps. In particular, \(f^ n_{r,q}\simeq *\) if either \(n>rq\) or \(r>\left( \begin{matrix} n\\ q\end{matrix} \right)\), and \(f^{rq}_{r,q}\) is the transfer associated to the wreath product inclusion \(\Sigma _ r\int \Sigma _ q\subset \Sigma _{rq}\). Some related results are also given.
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55Q25
Mathematics Subject Classification ID: 55R12
zbMATH DE Number: 3986180
zbMATH Keywords: Hopf invariants
zbMATH Keywords: transfer
zbMATH Keywords: stable decompositions of spaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3986180