Loop spaces of H-spaces with finitely generated cohomology

Yusuke Kawamoto

Vol. 190 (1999), No. 2, 311–328

DOI: 10.2140/pjm.1999.190.311

Abstract

Suppose X is a simply connected mod p H-space such that the mod p cohomology H^∗(ΩX) is a finitely generated algebra. We show that the loop space ΩX is homotopy equivalent to a finite product of Eilenberg-MacLane spaces K(ℤ,1), K(ℤ,2) and K(ℤ∕pⁱ,1) for i ≥ 1. This is a generalization of the result due to Lin, in which the same result was proved under the assumption that X is an A_p-space.

Milestones

Received: 2 January 1998

Revised: 5 August 1998

Published: 1 October 1999