On May spectral sequence and the algebraic transfer

Abstract

The algebraic transfer is an important tool to study the cohomology of the Steenrod algebra. In this study, we will construct a version of the algebraic transfer in E 2 -term of May spectral sequence and use this version to study the image of the algebraic transfer. By this method, we obtain the description of the image of ϕ s in some degrees.

On the determination of the Singer transfer

“…It is a useful tool in describing the homology groups of the Steenrod algebra, Tor A k,k+d (F 2 , F 2 ). This transfer was studied by Boardman [2], Bruner, Ha and Hung [3], Ha [5], Hung [9], Chon and Ha [4,10,11], Minami [12], Nam [7], Hung and Quynh [6], the present author [13] and others.…”

On the May spectral sequence and the algebraic transfer II

“…This note is a continuation of our previous paper [5], which we will refer to as Part I. In Part I, we use the May spectral sequence (MSS for short) to obtain new computation for the kernel and image of the algebraic transfer, introduced by Singer [19], which is an algebraic homomorphism …”

“…To overcome this difficulty, in this paper, we first dualize the construction in [5] to construct a representation of the algebraic transfer in the cohomological E 2 -term of the May spectral sequence. An application of this construction is given in Section 3.…”

“…The cohomology version which we are going to present has better behavior because of the algebra structure on Ext groups. Since the construction presented below is basically dual to that given in [5], we will be very brief.…”

“…In [4,5], we constructed and studied a representation of the dual of the algebraic transfer in the E 2 -term of the homology May spectral sequence. The cohomology version which we are going to present has better behavior because of the algebra structure on Ext groups.…”