Splitting of a simply connected Eilenberg–MacLane fibration ($H^{n+1}(B;G)=0\Rightarrow E{\simeq }_{\mathrm{w}}B\times K(G,n)$)

For a Serre fibration with this fiber over a simply connected CW base, the fiber identity class has only one possible nonzero outgoing differential in the cohomological Serre spectral sequence, landing in $H^{n+1}(B;G)$. If that group vanishes, the class extends to the CW total space. Its representing map, paired with projection to $B$, is an isomorphism on fiber and base homotopy groups and hence a weak homotopy equivalence to the product.