𝐴₂-annihilated elements in 𝐻_{*}(ΩΣ𝑅𝑃²)

Abstract

Let X n {X^n} denote the smash product of n n copies of R P 2 \mathbb {R}{\mathbb {P}^2} . We describe a minimal set of generators for H ∗ ( X n ; Z 2 ) {H^{\ast }}({X^n};{\mathbb {Z}_2}) as a module over the mod 2 \bmod \,2 Steenrod algebra. The description includes a procedure to obtain all of the generators, a generating function to enumerate them, and a proof of a nice conjecture about how many there are in each dimension.