The geometry of Deroin-Tholozan representations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913814251831296 |
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| author | Fenyes, Aaron Maret, Arnaud |
| author_facet | Fenyes, Aaron Maret, Arnaud |
| contents | We present a way to build hyperbolic spheres with conical singularities by gluing together simple building blocks. Our construction provides good control over the holonomy of the resulting hyperbolic cone sphere. In particular, it can be used to realize any Deroin-Tholozan (DT) representation as the holonomy of a hyperbolic cone sphere. Our construction is inspired by the correspondence between DT representations and chains of triangles in the hyperbolic plane. It gives a geometric interpretation of certain action-angle coordinates on the space of DT representations, which come from this correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09199 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The geometry of Deroin-Tholozan representations Fenyes, Aaron Maret, Arnaud Geometric Topology 57M50, 20C15 We present a way to build hyperbolic spheres with conical singularities by gluing together simple building blocks. Our construction provides good control over the holonomy of the resulting hyperbolic cone sphere. In particular, it can be used to realize any Deroin-Tholozan (DT) representation as the holonomy of a hyperbolic cone sphere. Our construction is inspired by the correspondence between DT representations and chains of triangles in the hyperbolic plane. It gives a geometric interpretation of certain action-angle coordinates on the space of DT representations, which come from this correspondence. |
| title | The geometry of Deroin-Tholozan representations |
| topic | Geometric Topology 57M50, 20C15 |
| url | https://arxiv.org/abs/2312.09199 |