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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For a CW-complex $X$ and homotopy classes $[f_i] \in \pi_{l_i}(X)$ for $1 \leq i \leq s$, where $s \geq 2$, the higher Whitehead product is defined to be the set $$[f_1,...,f_s] := \{[\rho \circ \phi] ... • 188 10 votes 1 answer 629 views ### Whitehead product and a homotopy group of a wedge sum Note : this is a crosspost from the Mathematics StackExchange, as suggested by this meta post. Let X be an n-connected (n\geqslant1) CW-complex and Y be a k-connected (k\geqslant1) CW-... • 243 7 votes 0 answers 156 views ### "Relative Whitehead products" The notion of a relative Whitehead product exists in the literature and has been asked about before (e.g. here). I am trying to find out about a different product on relative homotopy classes which ... • 188 5 votes 1 answer 298 views ### CW Product via Whitehead map Product CW-complexes are defined via characteristic maps rather than from attaching maps, so via maps from \mathbb D^n rather than from \mathbb S^{n-1}, because we have the propriety that \mathbb ... • 263 16 votes 1 answer 543 views ### Whitehead products and Framed Manifolds The attaching map for the top cell of the torus S^n \times S^n is a map$$ [x,y]: S^{2n-1} \to S^n \vee S^n  where the notation is such that $x,y : S^n \to S^n \vee S^n$ are the two inclusions–––...
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This is a question about signs. Fix a based space $(X,x_0)$, a topological group $G$ acting on $X$ from the left, so that the basepoint $x_0$ is fixed, a based map $\alpha\colon S^p\to G$ ($p\geq1$)...