Rigidity of elliptic genera for non-spin manifolds

Michael Wiemeler

doi:10.2140/agt.2025.25.2083

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arXiv · 2212.01059

Rigidity of elliptic genera for non-spin manifolds

Michael Wiemeler

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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.

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Michael Wiemeler. 2022-12-02. Rigidity of elliptic genera for non-spin manifolds. https://doi.org/10.2140/agt.2025.25.2083

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