A result on the A and elliptic genera on non-spin manifolds with circle actions

✍ Scribed by Haydeé Herrera; Rafael Herrera

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 51 KB
• Volume: 335
• Category: Article
• ISSN: 1631-073X
• DOI: 10.1016/s1631-073x(02)02480-9

✦ Synopsis

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.