Nguyen Sum

On the hit problem for the polynomial algebra

slide: PDF.
video: comming soon.
abstract:
We study the problem of determining a minimal set of generators for the polynomial algebra \(P_k := \mathbb{F}_2[x_1,x_2,\ldots,x_k]\) as a module over the mod-2 Steenrod algebra, \(\mathcal{A}\). In this paper, we study a minimal set of generators for \(\mathcal{A}\)-module \(P_k\) in some so-call generic degrees and apply these results to explicitly determine the hit problem for \(k=4\).