With one factor homologically free over a PID, product homology is the graded tensor product.Suggest a slogan
Let \(X, Y\) be CW complexes, let \(R\) be a principal ideal domain, and suppose \(H_i(X;R)\) is a free \(R\)-module for every \(i\) (for example, \(R\) a field). Then for each \(k\) the cross product gives an isomorphism \[ \bigoplus_{i+j=k}H_{i}(X;R)\tensor_R H_{j}(Y;R) \xrightarrow{\ \sim\ } H_{k}(X\times Y;R) \] [@Hat02].
State the Kunneth isomorphism in the torsion-free case.