The image of Singer's fourth transfer
type: Item
instance of: scholarly article
title: The image of Singer's fourth transfer
zbMATH Open document ID: 1181.55016
author: Võ T. N. Quy`nh
author: Nguyen Hu'u Viet Hu'ng
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2009-12-22T00:00:00Z
review text: This paper builds on earlier work, by the first author and his collaborators, to complete the calculation of the image of the degree-four part of the algebraic transfer defined by \textit{W. M. Singer} [Math. Z. 202, No.~4, 493--523 (1989; Zbl 0687.55014)]. Singer's transfer maps to the cohomology of the Steenrod algebra, and its domain consists of the GL-coinvariants of the classes in the homology of an elementary abelian \(2\)-group that are annihilated by all positive-degree Steenrod operations. The conclusion from this paper is that the image of the degree-four transfer consists of all of the \(d, e, f\) and \(p\) families of elements, and none of the \(g\), \(D_3\) and \(p'\) families. Whether or not the transfer is injective in this degree is still an open question, but the authors ``are confident'' that it is.
reviewed by: Martin D. Crossley
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 55R12
zbMATH DE Number: 5651246
zbMATH Keywords: Steenrod algebra
zbMATH Keywords: homotopy groups of spheres
zbMATH Keywords: transfer
MaRDI profile type: Publication
full work available at URL: j.crma.2009.10.018
OpenAlex ID: W1979165019
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DOI: 10.1016/J.CRMA.2009.10.018
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description: scientific article; zbMATH DE number 5651246