Epstein-Poincaré surfaces for $G-$opers
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908800866320384 |
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| author | Lema, Joaquín |
| author_facet | Lema, Joaquín |
| contents | Given a complex, simple Lie group $G$ of adjoint type, we introduce the notion of an Epstein-Poincaré surface associated to a $G$-oper. These surfaces generalize Epstein's classical construction for $G=PGL_2 (\mathbb{C})$. As an application, we provide a criterion that ensures that the holonomy of the oper is $Δ-$Anosov. Finally, we discuss how the developing map of the oper interacts with domains of discontinuity of the holonomy (whenever Anosov) and the transversality properties it satisfies. Along the way, we provide a quick review of opers that we hope serves as a self-contained introduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09936 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Epstein-Poincaré surfaces for $G-$opers Lema, Joaquín Differential Geometry Geometric Topology Given a complex, simple Lie group $G$ of adjoint type, we introduce the notion of an Epstein-Poincaré surface associated to a $G$-oper. These surfaces generalize Epstein's classical construction for $G=PGL_2 (\mathbb{C})$. As an application, we provide a criterion that ensures that the holonomy of the oper is $Δ-$Anosov. Finally, we discuss how the developing map of the oper interacts with domains of discontinuity of the holonomy (whenever Anosov) and the transversality properties it satisfies. Along the way, we provide a quick review of opers that we hope serves as a self-contained introduction. |
| title | Epstein-Poincaré surfaces for $G-$opers |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2601.09936 |