Proofs of Two Conjectures of Gray involving the double Suspension

Stephen D Theriault

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6 Citations (Scopus)


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




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
Publication statusPublished - Sep 2003



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