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Higher homotopy commutativity and cohomology of finite H-spaces

Yutaka Hemmi·Yusuke Kawamoto
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Abstract

We study connected mod p finite A_p-spaces admitting AC_n-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 A_p-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 AC_n-space structure compatible with the A_p-space structure.

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Yutaka Hemmi, Yusuke Kawamoto. 2004-08-17. Higher homotopy commutativity and cohomology of finite H-spaces. https://doi.org/10.1215/21562261-3664941

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