Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Proofs of two conjectures of Gray involving the double suspension

Author: Stephen D. Theriault
Journal: Proc. Amer. Math. Soc. 131 (2003), 2953-2962
MSC (2000): Primary 55P40; Secondary 55R35
Published electronically: January 28, 2003
MathSciNet review: 1974354
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

\begin{displaymath}{S^{2n-1}}\xrightarrow{E^{2}}{\Omega^{2} S^{2n+1}}\xrightarrow{f} {BW_{n}}\end{displaymath}


\begin{displaymath}{BW_{n}}\rightarrow{\Omega S^{2np+1}}\xrightarrow{\phi}{S^{2np-1}}.\end{displaymath}

He conjectured that $E^{2}\circ\phi$ 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 $p\geq 5$. Gray also conjectured that at odd primes $f$ factors through a map


We show that this is true as well when $p\geq 5$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55P40, 55R35

Retrieve articles in all journals with MSC (2000): 55P40, 55R35

Additional Information

Stephen D. Theriault
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Address at time of publication: Department of Mathematical Sciences, University of Aberdeen, Aberdeen, AB24 3UE, United Kingdom

Keywords: $p^{th}$-power map, double suspension
Received by editor(s): September 28, 2001
Received by editor(s) in revised form: April 2, 2002
Published electronically: January 28, 2003
Communicated by: Paul Goerss
Article copyright: © Copyright 2003 American Mathematical Society