Space of circle patterns on tori and its symplectic form
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929381082923008 |
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| author | Lam, Wai Yeung |
| author_facet | Lam, Wai Yeung |
| contents | We consider circle patterns on closed tori equipped with complex projective structures. There is an embedding of the space of circle patterns to the Teichmüller space of a punctured surface. Via the embedding, the Weil-Petersson symplectic form is pulled back to the space of circle patterns. We investigate its non-degeneracy. On the other hand, we also complete a conjecture that the space of circle patterns is homeomorphic to the Teichmüller space of the closed torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06733 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Space of circle patterns on tori and its symplectic form Lam, Wai Yeung Geometric Topology Complex Variables Differential Geometry We consider circle patterns on closed tori equipped with complex projective structures. There is an embedding of the space of circle patterns to the Teichmüller space of a punctured surface. Via the embedding, the Weil-Petersson symplectic form is pulled back to the space of circle patterns. We investigate its non-degeneracy. On the other hand, we also complete a conjecture that the space of circle patterns is homeomorphic to the Teichmüller space of the closed torus. |
| title | Space of circle patterns on tori and its symplectic form |
| topic | Geometric Topology Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2406.06733 |