The image of Singer's fourth transfer
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.
scientific article; zbMATH DE number 5651246