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arXiv · 2601.09936

Epstein-Poincar\'e surfaces for $G-$opers

Joaquín Lema
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Abstract

Given a complex, simple Lie group $G$ of adjoint type, we introduce the notion of an Epstein-Poincar\'e 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 $\Delta-$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.

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Joaquín Lema. 2026-01-14. Epstein-Poincar\'e surfaces for $G-$opers. https://arxiv.org/abs/2601.09936

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