A conjecture of Gray and the 𝑝-th power map on Ω²𝑆^{2𝑛𝑝+1}

Richter, William

doi:10.1090/S0002-9939-2014-11516-4

A conjecture of Gray and the $p$-th power map on $\Omega ^2 S^{2np+1}$
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Proc. Amer. Math. Soc. 142 (2014), 2151-2160 Request permission

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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