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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.02792 |
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| _version_ | 1866913974910451712 |
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| author | Tambe, Indraneel |
| author_facet | Tambe, Indraneel |
| contents | In this paper we use methods of Liu to show that the twisted Dirac operators $D$ on certain bundles $Φ$ considered by Guan and Wang are rigid. To do so, we use a Lefschetz formula and Atiyah-Bott localization to obtain formulas for the Lefschetz numbers $L$ of these operators $D$ in terms of Jacobi theta functions; then, using the translational and modular transformation properties of theta functions and the properties of their zeros, we prove $L$ is constant provided certain conditions on characteristic classes hold, thus showing the rigidity of $D$ on $Φ$ under these conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity via Modular Properties of Theta Functions Tambe, Indraneel Differential Geometry In this paper we use methods of Liu to show that the twisted Dirac operators $D$ on certain bundles $Φ$ considered by Guan and Wang are rigid. To do so, we use a Lefschetz formula and Atiyah-Bott localization to obtain formulas for the Lefschetz numbers $L$ of these operators $D$ in terms of Jacobi theta functions; then, using the translational and modular transformation properties of theta functions and the properties of their zeros, we prove $L$ is constant provided certain conditions on characteristic classes hold, thus showing the rigidity of $D$ on $Φ$ under these conditions. |
| title | Rigidity via Modular Properties of Theta Functions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.02792 |