Epstein-Poincar\'e surfaces for $G-$opers
Abstract
Given a complex, simple Lie group of adjoint type, we introduce the notion of an Epstein-Poincar\'e surface associated to a -oper. These surfaces generalize Epstein's classical construction for . As an application, we provide a criterion that ensures that the holonomy of the oper is 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.
Cite
@article{arxiv.2601.09936,
title = {Epstein-Poincar\'e surfaces for $G-$opers},
author = {Joaquín Lema},
journal= {arXiv preprint arXiv:2601.09936},
year = {2026}
}
Comments
v.2., eliminated discussion of lambda epstein surfaces, expanded applications, improved exposition in Section 4, fixed transversality discussion in the introduction. 46 pages, 4 pictures. Comments welcome!