Proofs of Two Conjectures of Gray involving the double Suspension

Stephen D Theriault

doi:10.1090/S0002-9939-03-06847-3

Proofs of Two Conjectures of Gray involving the double Suspension

Stephen D Theriault

Mathematical Science

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	2953-2962
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	131
DOIs	https://doi.org/10.1090/S0002-9939-03-06847-3
Publication status	Published - Sep 2003

Keywords

TORSION

Access to Document

10.1090/S0002-9939-03-06847-3

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

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