### Abstract

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

[GRAPHICS]

and

[GRAPHICS]

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 |
---|---|

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

*Proceedings of the American Mathematical Society*,

*131*, 2953-2962. https://doi.org/10.1090/S0002-9939-03-06847-3

**Proofs of Two Conjectures of Gray involving the double Suspension.** / Theriault, Stephen D.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Proofs of Two Conjectures of Gray involving the double Suspension

AU - Theriault, Stephen D

PY - 2003/9

Y1 - 2003/9

N2 - In proving that the fiber of the double suspension has a classifying space, Gray constructed fibrations[GRAPHICS]and[GRAPHICS]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.

AB - In proving that the fiber of the double suspension has a classifying space, Gray constructed fibrations[GRAPHICS]and[GRAPHICS]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.

KW - TORSION

U2 - 10.1090/S0002-9939-03-06847-3

DO - 10.1090/S0002-9939-03-06847-3

M3 - Article

VL - 131

SP - 2953

EP - 2962

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -