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A product on the homotopy groups of a space: $\pi_k(X)\times\pi_l(X) \to \pi_{k+l-1}(X)$.
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Accepted
Whitehead products and Framed Manifolds
By Pontryagin's Theorem, you are asking for the preimages of any chosen points
in each wedge factor of $S^p \vee S^q \vee S^r$ for the iterated Whitehead product map $p : S^{p+q+r-2} \to S^p \vee S^q …