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A conjecture of Gray and the $ p$-th power map on $ \Omega^2 S^{2np+1}$


Author: William Richter
Journal: Proc. Amer. Math. Soc. 142 (2014), 2151-2160
MSC (2010): Primary 55Q40, 55Q25
DOI: https://doi.org/10.1090/S0002-9939-2014-11516-4
Published electronically: February 27, 2014
MathSciNet review: 3182032
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Abstract: For $ p\ge 2$, the $ p$-th power map $ [p]$ on $ \Omega ^2 S^{2np+1}$ is homotopic to a composite $ \Omega ^2 S^{2np+1} \overset {\phi _n}{\longrightarrow } S^{2np-1} \overset {E^2}{\longrightarrow } \Omega ^2 S^{2np+1}, $ where the fiber of $ \phi _n$ is $ BW_n$.


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Additional Information

William Richter
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730
Email: richter@math.northwestern.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11516-4
Keywords: James-Hopf invariants, $BW_n$, Gray's conjecture, EHP sequence
Received by editor(s): October 21, 2010
Received by editor(s) in revised form: September 26, 2011, and October 2, 2011
Published electronically: February 27, 2014
Communicated by: Brooke Shipley
Article copyright: © Copyright 2014 American Mathematical Society