Volume 10 (2007)

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Higher homotopy commutativity and cohomology of finite H–spaces

Yutaka Hemmi and Yusuke Kawamoto

Geometry & Topology Monographs 10 (2007) 167–186

DOI: 10.2140/gtm.2007.10.167

arXiv: math.AT/0408215

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>(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.

Keywords

higher homotopy commutativity, H–spaces, Ap–spaces, ACn–spaces, Steenrod operations

Mathematical Subject Classification

Primary: 55P45, 57T25

Secondary: 55P48, 55S05

References
Publication

Received: 14 August 2004
Revised: 19 September 2005
Published: 29 January 2007

Authors
Yutaka Hemmi
Department of Mathematics
Faculty of Science
Kochi University
Kochi 780-8520
Japan
Yusuke Kawamoto
Department of Mathematics
National Defence Academy
Yokosuka 239-8686
Japan