We prove the vanishing of various characteristic numbers, such as the signature and the ̂A-genus, on manifolds with finite second homotopy group and which admit smooth S1-actions. More precisely, we prove the vanishing of various coefficientes of the elliptic genus on non-spin π2-finite manifolds when the S1-action either satisfies a "parity" condition or has isolated fixed points only. © 2003 Elsevier B.V. All rights reserved.
Herrera, H., & Herrera, R. (2004). The signature and the elliptic genus of π2-finite manifolds with circle actions. Topology and Its Applications, 136(1–3), 251–259. https://doi.org/10.1016/S0166-8641(03)00260-8