The previous chapter constructed spaces with a single nonzero homotopy group. We now connect these spaces to homology and cohomology. Hurewicz’s Theorem identifies the first nonzero homotopy group of a simply connected space with its first nonzero reduced homology group. This lets us choose a distinguished cohomology class on \(K(G,n)\text{;}\) pulling back that class will identify maps into \(K(G,n)\) with cohomology classes.
