= Samelson product
{c}
{title2=$\langle a,b\rangle$}
For sphere maps into a loop space or a group-like homotopy-associative space, take their pointwise <commutator>. It is trivial on the <wedge sum> of the two sphere factors, so descends to their smash product and defines $\langle a,b\rangle\in\pi_{p+q}(\Omega Y)$. This product obeys graded antisymmetry and the graded Jacobi identity. <Suspension-loop adjunction> identifies it with the sign-adjusted <Whitehead product>. Under the <Hurewicz homomorphism> it becomes the graded <commutator> of the <Pontryagin product>.
Back to article page
