Simple-stable representations of surface groups in $\mathrm{PU}(2,1)$
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914609592532992 |
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| author | Remfort-Aurat, Ulysse |
| author_facet | Remfort-Aurat, Ulysse |
| contents | Let $Γ_g$ be the fundamental group of a closed orientable surface of genus $g\geqslant 2$. The outer automorphism group $\mathrm{Out}(Γ_g)$ naturally acts on the character variety $\mathcal{X}(Γ_g,G)$ for any Lie group $G$. We consider the set of simple-stable representations which are modelled on Minsky's primitive-stable representations. We prove that the set of conjugacy classes of simple-stable representations of $Γ_g$ in $\mathrm{PU}(2,1)$ is a domain of discontinuity for this action, strictly larger than the set of conjugacy classes of convex cocompact representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28891 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simple-stable representations of surface groups in $\mathrm{PU}(2,1)$ Remfort-Aurat, Ulysse Geometric Topology Let $Γ_g$ be the fundamental group of a closed orientable surface of genus $g\geqslant 2$. The outer automorphism group $\mathrm{Out}(Γ_g)$ naturally acts on the character variety $\mathcal{X}(Γ_g,G)$ for any Lie group $G$. We consider the set of simple-stable representations which are modelled on Minsky's primitive-stable representations. We prove that the set of conjugacy classes of simple-stable representations of $Γ_g$ in $\mathrm{PU}(2,1)$ is a domain of discontinuity for this action, strictly larger than the set of conjugacy classes of convex cocompact representations. |
| title | Simple-stable representations of surface groups in $\mathrm{PU}(2,1)$ |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2605.28891 |