### Abstract

In proving that the fiber of the double suspension has a classifying space, Gray constructed fibrations

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and

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He conjectured that E-2 circle phi is homotopic to the p(th)-power map on Omega(2)S(2np+1) when p is an odd prime. Harper proved this is true when looped once. We remove the loop when p greater than or equal to 5. Gray also conjectured that at odd primes f factors through a map OmegaS(2n+1) {p} --> BWn. We show that this is true as well when p greater than or equal to 5.

Original language | English |
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Pages (from-to) | 2953-2962 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 131 |

DOIs | |

Publication status | Published - Sep 2003 |

### Keywords

- TORSION

## Cite this

Theriault, S. D. (2003). Proofs of Two Conjectures of Gray involving the double Suspension.

*Proceedings of the American Mathematical Society*,*131*, 2953-2962. https://doi.org/10.1090/S0002-9939-03-06847-3