Rigidity of elliptic genera for non-spin manifolds

TL;DR

This paper investigates the conditions under which elliptic genera remain rigid for non-spin manifolds with circle actions, revealing that universal covering spin condition ensures rigidity, but no simple condition on $\

Contribution

It establishes new criteria for the rigidity of elliptic genera in non-spin manifolds, linking it to the spin property of the universal cover, and shows limitations of $\

Findings

Universal elliptic genus is rigid if the universal cover is spin.

No simple $\

paper_type":"theoretical"} }

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.