Positively curved $ {\pi }_{2}$-finite manifolds

Haydeé Herrera

doi:10.1016/j.crma.2007.10.021

Differential Geometry

Positively curved

π_{2}

-finite manifolds

Presented by: Étienne Ghys

Haydeé Herrera ¹

¹ Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA

Comptes Rendus. Mathématique, Volume 345 (2007) no. 9, pp. 499-502.

Abstract
Résumé

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 $\hat{A} (M, T M)$ if G contains two commuting involutions.

Soit M une variété lisse avec un deuxième groupe d'homotopie fini, de courbure sectionnelle positive et de dimension plus grande que 8. Soit G un groupe de Lie compact et connexe qui agit de façon $C^{\infty}$ sur M. On démontre que le nombre caractéristique $\hat{A} (M, T M)$ s'annule si G contient deux involutions qui commutent entre elles.

Received: 2006-02-08
Accepted: 2007-10-03
Published online: 2007-11-01

DOI: 10.1016/j.crma.2007.10.021

Author's affiliations:

Haydeé Herrera ¹

¹ Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA

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     title = {Positively curved $ {\pi }_{2}$-finite manifolds},
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Haydeé Herrera. Positively curved $ {\pi }_{2}$-finite manifolds. Comptes Rendus. Mathématique, Volume 345 (2007) no. 9, pp. 499-502. doi : 10.1016/j.crma.2007.10.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.021/

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