Connected components of the space of type-preserving representations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916839991279616 |
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| author | Ryu, Inyoung Yang, Tian |
| author_facet | Ryu, Inyoung Yang, Tian |
| contents | We complete the characterization of the connected components of the space of type-preserving representations of a punctured surface group into $\mathrm{PSL}(2,\mathbb{R})$. We show that the connected components are indexed by the relative Euler classes and the signs of the images of the peripheral elements satisfying a generalized Milnor-Wood inequality; and when the surface is a punctured sphere, there are additional connected components consisting of ``totally non-hyperbolic" representations. As a consequence, we count the total number of the connected components of the space of type-preserving representations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_07391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connected components of the space of type-preserving representations Ryu, Inyoung Yang, Tian Geometric Topology 57K20, 57M05, 57M50 We complete the characterization of the connected components of the space of type-preserving representations of a punctured surface group into $\mathrm{PSL}(2,\mathbb{R})$. We show that the connected components are indexed by the relative Euler classes and the signs of the images of the peripheral elements satisfying a generalized Milnor-Wood inequality; and when the surface is a punctured sphere, there are additional connected components consisting of ``totally non-hyperbolic" representations. As a consequence, we count the total number of the connected components of the space of type-preserving representations. |
| title | Connected components of the space of type-preserving representations |
| topic | Geometric Topology 57K20, 57M05, 57M50 |
| url | https://arxiv.org/abs/2507.07391 |