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)

 

 

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


Author: Albert Shar
Journal: Proc. Amer. Math. Soc. 34 (1972), 303-306
MSC: Primary 55E40
MathSciNet review: 0292079
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55E40

Retrieve articles in all journals with MSC: 55E40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0292079-8
Keywords: Reduced product space, extensions, Whitehead products, Hopf invariant
Article copyright: © Copyright 1972 American Mathematical Society