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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] ...

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 ...

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 $\alpha\colon S^p\to G$ ($p\geq1$)...