THE HIT PROBLEM FOR THE POLYNOMIAL ALGEBRA OF FIVE VARIABLES IN A FAMILY OF GENERIC DEGREE

Abstract

Let E be an elementary abelian z-group oi rank k and let 13 E be the classitying space ot Ek. Then, the cohomology algebra Pk — H*(BEk-,W-2) is a polynomial algebra over the field F2 with two elements in k generators X1,X2,... ,Xk, with the degree of each Xi being 1. Hence, this algebra is a module over the mod-2 Steenrod algebra, A.
The hit problem of Frank Peterson asks for a minimal generating set for the polynomial algebra Pfc as a module over the mod-2 Steenrod algebra A. Equivalently, we want to find a vector space basis for F2 Pk hi each degree. This is an open problem in Algebraic Topology.
In this paper, we explicitly determine a minimal set of A-generators for P5 in terms of the admissible monomials for the case of the generic degree m = 2“+1 + 2d — 2 with d 6.