Homology, Homotopy and Applications
Volume 12 (2010)
Torsion in finite H-spaces and the homotopy of the three-sphere
Pages: 25 – 37
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 $i$: $S^3 →X$ has the property that the loop of its three-connected cover is null homotopic. In particular, such a null homotopy implies that $π_m(i)=0 for m ≥4$. Applications are made to Harper’s rank 2 finite $H$-space and simple, simply-connected, compact Lie groups.
$H$-space; Harper’s space; torsion Lie group; three sphere
2010 Mathematics Subject Classification