Hopf invariants for reduced products of spheres

Baues, Hans Joachim

doi:10.1090/S0002-9939-1976-0420616-2

Hopf invariants for reduced products of spheres
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Proc. Amer. Math. Soc. 59 (1976), 169-174 Request permission

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 \[ H_m^n:{\pi _{mn - 1}}(S_{m - 1}^n) \to {\mathbf {Z}}\] 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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Über die Abbilungen von Sphären auf Sphären niedrigerer Dimension

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