Abstract
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: $S^3 \underset {\longrightarrow}{i} X$ has the property that the loop of its three-connected cover is null homotopic. In particular, such a null homotopy implies that $\pi_m(i )= 0$ for $m \geq 4$. Applications are made to Harper's rank 2 finite $H$-space and simple, simply-connected, compact Lie groups.
Citation
Piotr Beben. Stephen Theriault. "Torsion in finite $H$-spaces and the homotopy of the three-sphere." Homology Homotopy Appl. 12 (2) 25 - 37, 2010.
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