𝜋_{𝑚𝑛-}2(𝑆ⁿ_{𝑚-}2) contains an element of order 𝑚

Shar, Albert

doi:10.1090/S0002-9939-1972-0292079-8

$\pi _{mn-}{}_{}{2}(S^{n}_{m-}{}_{}{2})$ contains an element of order $m$
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by Albert Shar PDF

Proc. Amer. Math. Soc. 34 (1972), 303-306 Request permission

Abstract:

Let $S_m^n$ be the mth reduced product complex of ${S^n}$ with n an even integer greater than 2 and m any integer greater than 2. $S_m^n = S_{m - 1}^n \cup {e^{nm}}$ with attaching map $[i, \cdots ,i] \in {\pi _{nm - 1}}(S_{m - 1}^n)$. Using a result of J. R. Hubbuck and a result of the author it is proven that the Whitehead product $[i,[i, \cdots ,i]] \in {\pi _{mn - 2}}(S_{m - 2}^n)$ is of order m.

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