A result on the 𝐀 ^ and elliptic genera on non-spin manifolds with circle actions
Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 371-374.

We prove the vanishing of the 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.

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 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.

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

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