Positively curved [formula omitted]-finite manifolds

Abstract

Let M be a smooth manifold with finite second homotopy group, positive sectional curvature, dimension greater than 8, and assume that a compact connected Lie group G acts smoothly on M. We prove the vanishing of the characteristic number A ˆ ( M , T M ) if G contains two commuting involutions. To cite this article: H. Herrera, C. R. Acad. Sci. Paris, Ser. I 345 (2007).