Let X be a 2-connected p-local finite H-space with a single cell in dimension three. We give a simple cohomological criterion which distinguishes when the inclusion i: S3→X has the property that the loop of its three-connected cover is null homotopic. In particular, such a null homotopy implies that πm(i)=0 for m ≥ 4. Applications are made to Harper's rank 2 finite H-space and simple, simply-connected, compact Lie groups.
Homology, Homotopy and Applications, Vol. 12 (2010), No. 2, pp.25-37.
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