Comptes Rendus
Geometry/Topology
The Aˆ-genus of S1-manifolds with finite second homotopy group
[Le Aˆ-genre de S1-variétés avec le deuxième groupe homotopie fin]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 283-285.

Nous construisons des variétés M simplement connexes de dimension 4k8 avec les propriétés suivantes : le deuxième groupe d'homotopie π2(M) est fini, M admet une action lisse du cercle S1 et le Aˆ-genre Aˆ(M) est non nulle.

We construct simply connected smooth manifolds M of dimension 4k8 with the following properties: the second homotopy group π2(M) is finite, M admits a smooth action by the circle S1 and the Aˆ-genus Aˆ(M) is non-zero.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.01.011

Manuel Amann 1 ; Anand Dessai 2

1 University of Münster, Department of Mathematics, Einsteinstraße 62, 48149 Münster, Germany
2 University of Fribourg, Department of Mathematics, Chemin du Musée 23, CH-1700 Fribourg, Switzerland
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Manuel Amann; Anand Dessai. The $ \stackrel{ˆ}{A}$-genus of $ {S}^{1}$-manifolds with finite second homotopy group. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 283-285. doi : 10.1016/j.crma.2010.01.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.01.011/

[1] M.F. Atiyah; F. Hirzebruch Spin-manifolds and group actions, Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, 1970, pp. 18-28

[2] A. Borel; F. Hirzebruch Characteristic classes and homogeneous spaces. II, Amer. J. Math., Volume 81 (1959), pp. 315-382

[3] R. Bott; C. Taubes On the rigidity theorems of Witten, J. Amer. Math. Soc., Volume 2 (1989), pp. 137-186

[4] G.E. Bredon Representations at fixed points of smooth actions of compact groups, Ann. of Math. (2), Volume 89 (1969), pp. 515-532

[5] W. Browder Surgery on Simply Connected Manifolds, Springer, 1972

[6] H. Herrera; R. Herrera Aˆ-genus on non-spin manifolds with S1 actions and the classification of positive quaternion-Kähler 12-manifolds, J. Differential Geom., Volume 61 (2002), pp. 341-364

[7] H. Herrera, R. Herrera, Erratum to [6], in press

[8] F. Hirzebruch; P. Slodowy Elliptic genera, involutions and homogeneous spin manifolds, Geom. Dedicata, Volume 35 (1990), pp. 309-343

[9] S. Salamon Quaternion-Kähler geometry, Essays on Einstein Manifolds, Surveys in Differential Geometry, vol. VI, Int. Press, 1999, pp. 83-121

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