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Higher homotopy commutativity and cohomology of finite H-spaces

Yutaka Hemmi, Yusuke Kawamoto

Published 2004-08-17, updated 2009-03-25Version 2

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.

Comments: This is the version published by Geometry & Topology Monographs on 29 January 2007
Journal: Geom. Topol. Monogr. 10 (2007) 167-186
Categories: math.AT
Subjects: 55P45, 57T25, 55P48, 55S05
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