Comptes Rendus
no. 1
Differential Geometry
Circle actions and Z/k-manifolds
[Actions du cercle et Z/k variétés]

Présenté par : Jean-Michel Bismut

Weiping Zhang1
1 Nankai Institute of Mathematics, Nankai University, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Volume 337 (2003) no. 1, pp. 57-60.

On établit un théorème d'indice S1-équivariant pour les opérateurs de Dirac sur des Z/k variétés. On donne une application de ce résultat, qui généralise le théorème d'Atiyah–Hirzebruch sur les actions de S1 aux Z/k variétés.

We establish an S1-equivariant index theorem for Dirac operators on Z/k-manifolds. As an application, we generalize the Atiyah–Hirzebruch vanishing theorem for S1-actions on closed spin manifolds to the case of Z/k-manifolds.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00279-6

Weiping Zhang 1

1 Nankai Institute of Mathematics, Nankai University, Tianjin 300071, PR China 
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Weiping Zhang. Circle actions and $ \mathrm{Z}\mathrm{/k}$-manifolds. Comptes Rendus. Mathématique, Volume 337 (2003) no. 1, pp. 57-60. doi : 10.1016/S1631-073X(03)00279-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00279-6/

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