Rigidity of elliptic genera for non-spin manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912542035542016 |
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| author | Wiemeler, Michael |
| author_facet | Wiemeler, Michael |
| contents | 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 $π_2(M)$ that guarantees the rigidity in the case that the universal covering of $M$ is non-spin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01059 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rigidity of elliptic genera for non-spin manifolds Wiemeler, Michael Geometric Topology 53C27, 57R15, 57R91, 57S15, 58J26 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 $π_2(M)$ that guarantees the rigidity in the case that the universal covering of $M$ is non-spin. |
| title | Rigidity of elliptic genera for non-spin manifolds |
| topic | Geometric Topology 53C27, 57R15, 57R91, 57S15, 58J26 |
| url | https://arxiv.org/abs/2212.01059 |