Rigidity of elliptic genera for non-spin manifolds

Abstract

We discuss the rigidity of elliptic genera for non-spin manifolds $M$ with $S^1$-action. We show that if the universal covering of $M$ is spin, then the universal elliptic genus of $M$ is rigid. Moreover, we show that there is no condition which only depends on ${\pi }_2(M)$ that guarantees the rigidity in the case that the universal covering of $M$ is non-spin.

14 pages, minor changes, to appear in AGT

References in corpus (1)

• $S^1$-equivariant bordism, invariant metrics of positive scalar curvature, and rigidity of elliptic genera

Cited by in corpus (1)

• Circle actions on six dimensional oriented manifolds with isolated fixed points