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Comptes Rendus Mathématique
Volume 335, n° 4
pages 371-374 (2002)
Doi : S1631-073X(02)02480-9
Received : 12 April 2002 ;  accepted : 27 May 2002
A result on the A and elliptic genera on non-spin manifolds with circle actions
Un résultat sur les variétés non-spinorielles de genres A et elliptique munies d'actions de S 1
 

Haydeé Herrera a , Rafael Herrera b
a Department of Mathematics, Tufts University, Medford, MA 02155, USA 
b Department of Mathematics, University of California, Riverside, CA 92521, USA 

Note presented by Mikhaël Gromov

Abstract

We prove the vanishing of the A-genus of compact smooth manifolds with finite second homotopy group and endowed with smooth S 1 actions. These manifolds are not necessarily spin, hence, this vanishing extends that of Atiyah and Hirzebruch on spin manifolds with S 1 actions. The proof is accomplished by proving a rigidity theorem under circle actions of the elliptic genus on these manifolds. To cite this article: H. Herrera, R. Herrera, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 371-374.

The full text of this article is available in PDF format.
Résumé

On montre que le A-genre d'une variété lisse, compacte munie d'un second groupe d'homotopie fini et dotée d'une action de S 1 est égal à zéro. Ces variétés ne sont pas nécessairement spinorielles de sorte que ce théorème d'annulation étend le résultat d'Atiyah-Hirzebruch établi pour des variétés spinorielles avec actions de S 1. La démonstration est faite à partir d'un théorème de rigidité sous des actions de S 1 de genre elliptique sur ces variétés. Pour citer cet article : H. Herrera, R. Herrera, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 371-374.

The full text of this article is available in PDF format.


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