Deformation rigidity for Z/2 eigensections
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911604360085504 |
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| author | Haydys, Andriy He, Siqi Salm, Willem Adriaan |
| author_facet | Haydys, Andriy He, Siqi Salm, Willem Adriaan |
| contents | We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that every minimal non-degenerate critical eigensection is deformation rigid: any sufficiently small deformation of the configuration that still admits a critical eigensection must come from an SO(3)-rotation. This generalizes the rigidity phenomenon previously discovered in symmetric examples of Taubes-Wu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17044 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformation rigidity for Z/2 eigensections Haydys, Andriy He, Siqi Salm, Willem Adriaan Differential Geometry 53C99 We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that every minimal non-degenerate critical eigensection is deformation rigid: any sufficiently small deformation of the configuration that still admits a critical eigensection must come from an SO(3)-rotation. This generalizes the rigidity phenomenon previously discovered in symmetric examples of Taubes-Wu. |
| title | Deformation rigidity for Z/2 eigensections |
| topic | Differential Geometry 53C99 |
| url | https://arxiv.org/abs/2604.17044 |