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Proceedings of the American Mathematical Society

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

 
 

 

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


Author: Albert Shar
Journal: Proc. Amer. Math. Soc. 34 (1972), 303-306
MSC: Primary 55E40
DOI: https://doi.org/10.1090/S0002-9939-1972-0292079-8
MathSciNet review: 0292079
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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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Keywords: Reduced product space, extensions, Whitehead products, Hopf invariant
Article copyright: © Copyright 1972 American Mathematical Society