The $ \stackrel{ˆ}{A}$-genus of $ {S}^{1}$-manifolds with finite second homotopy group

Amann, Manuel; Dessai, Anand

doi:10.1016/j.crma.2010.01.011

Geometry/Topology

The

\hat{A}

-genus of

S^{1}

-manifolds with finite second homotopy group
[Le

\hat{A}

-genre de

S^{1}

-variétés avec le deuxième groupe homotopie fin]

Présenté par : Jean-Pierre Demailly

Amann, Manuel ¹ ; Dessai, Anand 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

Comptes Rendus. Mathématique, Tome 348 (2010) no. 5-6, pp. 283-285.

Résumé
Abstract

Nous construisons des variétés M simplement connexes de dimension $4 k ⩾ 8$ avec les propriétés suivantes : le deuxième groupe d'homotopie $π_{2} (M)$ est fini, M admet une action lisse du cercle $S^{1}$ et le $\hat{A}$ -genre $\hat{A} (M)$ est non nulle.

We construct simply connected smooth manifolds M of dimension $4 k ⩾ 8$ with the following properties: the second homotopy group $π_{2} (M)$ is finite, M admits a smooth action by the circle $S^{1}$ and the $\hat{A}$ -genus $\hat{A} (M)$ is non-zero.

Reçu le : 2009-09-29
Accepté le : 2010-01-09
Publié le : 2010-02-19

DOI : 10.1016/j.crma.2010.01.011

Affiliations des auteurs :

Amann, Manuel ¹ ; Dessai, Anand ²

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     author = {Amann, Manuel and Dessai, Anand},
     title = {The $ \stackrel{{\textasciicircum}}{A}$-genus of $ {S}^{1}$-manifolds with finite second homotopy group},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {283--285},
     publisher = {Elsevier},
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     doi = {10.1016/j.crma.2010.01.011},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2010.01.011/}
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Amann, Manuel; Dessai, Anand. The $ \stackrel{ˆ}{A}$-genus of $ {S}^{1}$-manifolds with finite second homotopy group. Comptes Rendus. Mathématique, Tome 348 (2010) no. 5-6, pp. 283-285. doi : 10.1016/j.crma.2010.01.011. http://www.numdam.org/articles/10.1016/j.crma.2010.01.011/

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