On the computation of ${\mathrm{Ext}}_{\mathcal{A}}^{k,k+\ast }(\mathbb{Z}/2,\mathbb{Z}/2)$ for $k\le 5$

Abstract

This Note presents a computational algorithm for determining a basis of the cohomology of the mod 2 Steenrod algebra, ${\mathrm{Ext}}_{\mathcal{A}}^{k,k+\ast }(\mathbb{Z}/2,\mathbb{Z}/2)$ for $k\le 5$, based on the well-known generators and the Adams relations given in Chen's work [2]. The purpose of this algorithm is to verify the hand-computed results for ${\mathrm{Ext}}_{\mathcal{A}}^{4,4+\ast }(\mathbb{Z}/2,\mathbb{Z}/2)$ presented in our corrected papers [8, 9, 10]. Combining our most recent works [11, 12], the verification of the domain and the codomain of the fourth algebraic transfer in specific degrees can now be completed.

arXiv comment21 pages. Any constructive suggestions are most welcome