Higher homotopy commutativity of H-spaces with finitely generated cohomology

Yusuke Kawamoto

Vol. 204 (2002), No. 1, 145–161

DOI: 10.2140/pjm.2002.204.145

Abstract

Suppose X is a simply connected mod p H-space such that the mod p cohomology H^∗(X; ℤ∕p) is finitely generated as an algebra. Our first result shows that if X is an A_n-space, then X is the total space of a principal A_n-fibration with base a finite A_n-space and fiber a finite product of ℂP^∞s. As an application of the first result, it is shown that if X is a quasi C_p-space, then X is homotopy equivalent to a finite product of ℂP^∞s.

Milestones

Received: 14 July 2000

Revised: 3 July 2001

Published: 1 May 2002