Proofs of Two Conjectures of Gray involving the double Suspension

Stephen D Theriault

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish
Pages (from-to)2953-2962
Number of pages9
JournalProceedings of the American Mathematical Society
Volume131
DOIs
Publication statusPublished - Sep 2003

Keywords

  • TORSION

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 131, 09.2003, p. 2953-2962.

Research output: Contribution to journalArticle

@article{6d60d4f840014aee8ba62429d89004f8,
title = "Proofs of Two Conjectures of Gray involving the double Suspension",
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.",
keywords = "TORSION",
author = "Theriault, {Stephen D}",
year = "2003",
month = "9",
doi = "10.1090/S0002-9939-03-06847-3",
language = "English",
volume = "131",
pages = "2953--2962",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",

}

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 -