arXiv subjects

Joaquín Lema

Publications and source records attributed to Joaquín Lema.

3 recordsLinked to original sources

arXiv2026

On separated families of Anosov representations

We introduce different notions of separation for families of Anosov representations. We show that, along a diverging sequence of such families, the critical exponent is asymptotic to a combinatorial invariant computable from the spectral data of a finite graph. Our method allows us to derive bounds on the Thurston asymmetric metric. As an application, we study specific degenerations of convex projective structures on a pair of pants, generalizing an example of McMullen.

math.GT↗

arXiv2026

Epstein-Poincaré surfaces for $G-$opers

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.

math.DG↗

arXiv2022

Uniform foliations with Reeb components

A foliation on a compact manifold is uniform if each pair of leaves of the induced foliation on the universal cover are at finite Hausdorff distance from each other. We study uniform foliations with Reeb components. We give examples of such foliations on a family of closed $3-$manifolds with infinite fundamental group. Furthermore, we prove some results concerning the behavior of a uniform foliation with Reeb components on general $3-$manifolds.

math.GT↗