2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173474We construct examples of $S^1$-manifolds with finite second homotopy group and non-vanishing $\hat A$-genus. This is related to the classification of positive quaternionic Kaehler manifolds.Differential GeometryA note on the $\hat A$-genus for $π_2$-finite manifolds with $S^1$-symmetrytext