no. 9
Differential Geometry
Positively curved π2-finite manifolds
[Variétés avec π2 fini et courbure positive]

Présenté par : Étienne Ghys

Herrera, Haydeé1
1 Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA
Comptes Rendus. Mathématique, Tome 345 (2007) no. 9, pp. 499-502.

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∞ sur M. On démontre que le nombre caractéristique Aˆ(M,TM) s'annule si G contient deux involutions qui commutent entre elles.

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 Aˆ(M,TM) if G contains two commuting involutions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.10.021
Herrera, Haydeé 1

1 Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA 
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Herrera, Haydeé. Positively curved $ {\pi }_{2}$-finite manifolds. Comptes Rendus. Mathématique, Tome 345 (2007) no. 9, pp. 499-502. doi : 10.1016/j.crma.2007.10.021. http://www.numdam.org/articles/10.1016/j.crma.2007.10.021/

[1] Bott, R.; Taubes, T. On the rigidity theorems of Witten, J. Amer. Math. Soc., Volume 2 (1989) no. 1, pp. 137-186

[2] Dessai, A. Characteristic numbers of positively curved Spin-manifolds with symmetry, Proc. Amer. Math. Soc., Volume 133 (2005) no. 12, pp. 3657-3661

[3] Frankel, T. Manifolds with positive curvature, Pacific J. Math., Volume 11 (1961), pp. 165-174

[4] Herrera, H.; Herrera, R. Aˆ-genus on non-spin manifolds with S1 actions and the classification of positive quaternion-Kähler 12-manifolds, J. Differential Geom., Volume 61 (2002) no. 3, pp. 341-364

[5] Herrera, H.; Herrera, R. The signature and the elliptic genus of π2-finite manifolds with circle actions, Topology Appl., Volume 136 (2004) no. 1–3, pp. 251-259

[6] Hirzebruch, F.; Berger, T.; Jung, R. Manifolds and Modular Forms, Aspects of Mathematics, Vieweg, 1992

[7] Petrunin, A.; Tuschmann, W. Diffeomorphism finiteness, positive pinching, and second homotopy, Geom. Funct. Anal., Volume 9 (1999) no. 4, pp. 736-774

[8] Wilking, B. Torus actions on manifolds of positive sectional curvature, Acta Math., Volume 191 (2003) no. 2, pp. 259-297

[9] Witten, E. Elliptic genera and quantum field theory, Comm. Math. Phys., Volume 109 (1987), p. 525

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