Meyer, D. M.D. M.MeyerSmith, LarryLarrySmith2018-11-072018-11-072003https://resolver.sub.uni-goettingen.de/purl?gro-2/46794Let d(2,0) = x(2)y + xy(2), d(2,1) = x(2) + xy + y(2) is an element of F-2[x,y] be the two Dickson polynomials. If a and b are positive integers, the ideal (d(2,0)(a), d(2,1)(b)) subset of F-2[x, y] is invariant under the action of the mod 2 Steenrod algebra A if and only if when we write b = 2(t) . k with k odd, then a less than or equal to 2(t). The quotient algebra F-2[x, y]/(d(2,0)(a), d(2,1)(b)) is a Poincare duality algebra and for such a and b admits an unstable action of A . It has trivial Wu classes if and only if a = 2(t) for some t greater than or equal to 0 and b = 2(t)(2(s) - 1) for some s > 0. We ask under what conditions on a and b, F-2[x, y]/(d(2,0)(a), d(2,1)(b)) appears as the mod 2 cohomology of a manifold. In this note we show that for a = 2(t) = b there is a topological space whose cohomology is F-2[x,y]/(d(2,0)(2t), d(2,1)(2t)) if and only if t = 0, 1, 2, or 3, and in these cases the space may be taken to be a smooth manifold.journal_article10.4064/fm177-3-4000186509400004