Higher homotopy commutativity and cohomology of finite H-spaces
Abstract
We study connected mod p finite Ap-spaces admitting ACn-space structures with n<p for an odd prime p. Our result shows that if n is greator than (p-1)/2, then the mod p Steenrod algebra acts on the mod p cohomology of such a space in a systematic way. Moreover, we consider Ap-spaces which are mod p homotopy equivalent to product spaces of odd dimensional spheres. Then we determine the largest integer n for which such a space admits an ACn-space structure compatible with the Ap-space structure.
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