Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Faraco

Geometrization of purely hyperbolic representations in $\text{PSL}_2\Bbb R$

created by faraco on 09 Nov 2022


Published Paper

Inserted: 9 nov 2022
Last Updated: 9 nov 2022

Journal: Advances in Geometry
Year: 2021
Doi: DOI 10.1515/advgeom-2020-0025

ArXiv: 1712.03510 PDF


Let $S$ be a surface of genus $g$ at least $2$. A representation $\rho:\pi_1S\longrightarrow \text{PSL}_2\Bbb R$ is said to be purely hyperbolic if its image consists only of hyperbolic elements other than the identity. We may wonder under which conditions such representations arise as holonomy of a hyperbolic cone-structure on $S$. In this work we will characterize them completely, giving necessary and sufficient conditions.

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