### 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: S3i⟶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.

Original language | English |
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Pages (from-to) | 25-37 |

Number of pages | 13 |

Journal | Homology, Homotopy and Applications |

Volume | 12 |

Issue number | 2 |

Publication status | Published - 2010 |

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## Cite this

Beben, P., & Theriault, S. D. (2010). Torsion in finite H-spaces and the homotopy of the three-sphere.

*Homology, Homotopy and Applications*,*12*(2), 25-37. https://projecteuclid.org/euclid.hha/1296223877