On the subalgebra of \(H_*(({\mathbb{R}}\text{P}^\infty)^n;F_2)\) annihilated by Steenrod operations
Let \(A\) be the mod 2 Steenrod algebra and \(I\) be the augmentation ideal. We denote by \(P(n)= \mathbb{F}_2[x_1, \dots, x_n]\) the polynomial unstable \(A\)-algebra on generators of degree 1. In this paper the authors define a homomorphism \(\theta\) on \(P(n)\) such that \(\theta(I.P(n))=0\). They show that \(\text{Im} \theta\) (or its dual) is related to the problem of finding a basis for \(P(n)/I.P(n)\) [\textit{R. M. W. Wood}, Math. Proc. Camb. Philos. Soc. 105, No. 2, 307-309 (1989; Zbl 0692.55011)].
scientific article; zbMATH DE number 1308169