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Proceedings of the American Mathematical Society

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

 

 

Hopf invariants for reduced products of spheres


Author: Hans Joachim Baues
Journal: Proc. Amer. Math. Soc. 59 (1976), 169-174
MSC: Primary 55E25
DOI: https://doi.org/10.1090/S0002-9939-1976-0420616-2
MathSciNet review: 0420616
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Abstract: Let $ S_m^n$ be the $ m$th reduced product complex of the even dimensional sphere $ {S^n}$. Using 'cup'-products, James defined a Hopf invariant homomorphism

$\displaystyle H_m^n:{\pi _{mn - 1}}(S_{m - 1}^n) \to {\mathbf{Z}}$

such that $ H_2^n$ is the classical Hopf invariant. Extending the result of Adams on $ H_2^n$ we determine the image of $ H_m^n$. Partial calculations were made by Hardie and Shar.

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DOI: https://doi.org/10.1090/S0002-9939-1976-0420616-2
Keywords: Hopf invariant, Whitehead product, reduced product space
Article copyright: © Copyright 1976 American Mathematical Society