Steenrod operations on mod 2 homology of the iterated loop space
In Acta Math. Vietnam. 6, No.2, 41-48 (1981; Zbl 0518.20044) and ibid. 7, No.1, 95-100 (1982; Zbl 0571.55009), the second author introduced the Dickson characteristic classes derived from modular invariants and used them to determine the algebraic structure of \(H^*(\Omega^ q_ 0S^ q,Z/2)\) for \(0<q\leq \infty\). Here \(\Omega^ q_ 0S^ q\) denotes the component of the base point of the iterated loop space \(\Omega^ qS^ q.\) The purpose of this paper is to study the action of the opposite mod 2 Steenrod algebra \(A_*=A_*(2)\) on the homology \(H_*(\Omega^ q_ 0S^ q;Z/2)\) also by means of modular invariants and the Dickson classes. Roughly speaking, we will reduce this action to the usual action of the mod 2 Steenrod algebra \(A=A(2)\) on the Dickson algebra \(Z/2[x_ 1,...,x_ n]^{GL(n,Z/2)}\).
scientific article; zbMATH DE number 4111584