Mod 3 cohomology algebras of finite H -spaces

Abstract

Let X be a 3 local, finite, simply connected H-space with associative homology ring $H_* (X ; \mathbb F_3)$ . Some known examples are the Lie group $E_8$ , Harper's H-space X(3) and any odd dimensional sphere $S^{2n+1}$ . We prove the cohomology algebra $H^* (X; \mathbb F_3)$ is isomorphic to the cohomology algebra of a finite product of $E_8 s, X(3) s$ and odd dimensional spheres.