= Postnikov invariant
{c}
{title2=$k_n$}
= k-invariant
{synonym}
The $n$th <Postnikov invariant> is the <cohomology class> $k_n\in H^{n+1}(P_{n-1}X;\pi_nX)$ whose representing map has <homotopy fibre> $P_nX$. It specifies how the new <homotopy group> is attached to the previous stage. A zero invariant gives the product $P_nX\simeq P_{n-1}X\times K(\pi_nX,n)$. Merely tensoring <homotopy groups> with $\mathbb Q$ does not describe <rationalization of a topological space> unless these classes are also transported.
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