A result on the $ \hat{\mathbf{A}}$ and elliptic genera on non-spin manifolds with circle actions

Herrera, Haydeé; Herrera, Rafael

doi:10.1016/S1631-073X(02)02480-9

A result on the

\hat{𝐀}

and elliptic genera on non-spin manifolds with circle actions
[Un résultat sur les variétés non-spinorielles de genres

\hat{A}

et elliptique munies d'actions de S¹]

Herrera, Haydeé ¹ ; Herrera, Rafael ²

¹ Department of Mathematics, Tufts University, Medford, MA 02155, USA
² Department of Mathematics, University of California, Riverside, CA 92521, USA

Comptes Rendus. Mathématique, Tome 335 (2002) no. 4, pp. 371-374.

Résumé
Abstract

On montre que le $\hat{A}$ -genre d'une variété lisse, compacte munie d'un second groupe d'homotopie fini et dotée d'une action de S¹ 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 S¹. La démonstration est faite à partir d'un théorème de rigidité sous des actions de S¹ de genre elliptique sur ces variétés.

We prove the vanishing of the $\hat{A}$ -genus of compact smooth manifolds with finite second homotopy group and endowed with smooth S¹ actions. These manifolds are not necessarily spin, hence, this vanishing extends that of Atiyah and Hirzebruch on spin manifolds with S¹ actions. The proof is accomplished by proving a rigidity theorem under circle actions of the elliptic genus on these manifolds.

Reçu le : 2002-04-12
Accepté le : 2002-05-27
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02480-9

Affiliations des auteurs :

Herrera, Haydeé ¹ ; Herrera, Rafael ²

¹ Department of Mathematics, Tufts University, Medford, MA 02155, USA
² Department of Mathematics, University of California, Riverside, CA 92521, USA

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     title = {A result on the $ \hat{\mathbf{A}}$ and elliptic genera on non-spin manifolds with circle actions},
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Herrera, Haydeé; Herrera, Rafael. A result on the $ \hat{\mathbf{A}}$ and elliptic genera on non-spin manifolds with circle actions. Comptes Rendus. Mathématique, Tome 335 (2002) no. 4, pp. 371-374. doi : 10.1016/S1631-073X(02)02480-9. https://www.numdam.org/articles/10.1016/S1631-073X(02)02480-9/

Bibliographie
Cité par

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