The Space of Vectored Hyperbolic Surfaces is Path-Connected
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910579982073856 |
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| author | Warakkagun, Sangsan |
| author_facet | Warakkagun, Sangsan |
| contents | In the space $\mathcal{H}^2$ of hyperbolic surfaces decorated with a base unit vector, the topology induced by the Gromov-Hausdorff convergence coincides with the Chabauty topology on the space of discrete torsion-free subgroups of $\rm{PSL}_2(\mathbb{R})$. Using paths constructed from changing the Fenchel-Nielsen coordinates and shrinking simple closed curves to cusps, we demonstrate path-connectivity of $\mathcal{H}^2$ and some of its subspaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16667 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Space of Vectored Hyperbolic Surfaces is Path-Connected Warakkagun, Sangsan Geometric Topology 57K20 In the space $\mathcal{H}^2$ of hyperbolic surfaces decorated with a base unit vector, the topology induced by the Gromov-Hausdorff convergence coincides with the Chabauty topology on the space of discrete torsion-free subgroups of $\rm{PSL}_2(\mathbb{R})$. Using paths constructed from changing the Fenchel-Nielsen coordinates and shrinking simple closed curves to cusps, we demonstrate path-connectivity of $\mathcal{H}^2$ and some of its subspaces. |
| title | The Space of Vectored Hyperbolic Surfaces is Path-Connected |
| topic | Geometric Topology 57K20 |
| url | https://arxiv.org/abs/2311.16667 |