Whitehead product

In mathematics, the Whitehead product is a graded quasi-Lie algebra structure on the homotopy groups of a space. It was defined by J. H. C. Whitehead in (Whitehead 1941).

Given elements ${\displaystyle f\in \pi _{k}(X),g\in \pi _{l}(X)}$, the Whitehead bracket

is defined as follows:

The product ${\displaystyle S^{k}\times S^{l}}$ can be obtained by attaching a ${\displaystyle (k+l)}$-cell to the wedge sum

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