Rational Whitehead theorem ($H_{\ast }(f;\mathbb{Q})\text{ invertible}\Rightarrow {\pi }_{\ast }(f)\otimes \mathbb{Q}\text{ invertible}$)

For maps between simply connected spaces, a rational homology equivalence is a rational homotopy equivalence. It follows from the relative Hurewicz theorem modulo torsion, or from rationalization and the homological Whitehead theorem.