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

Gianluca Faraco

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

Geometric Topology 2019-05-27 v3

Authors: Gianluca Faraco

Abstract

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.

Keywords

purely hyperbolic representation PSL_2 R hyperbolic cone-structure holonomy surface necessary and sufficient conditions

Cite

@article{arxiv.1712.03510,
  title  = {Geometrization of purely hyperbolic representations in $\text{PSL}_2\Bbb R$},
  author = {Gianluca Faraco},
  journal= {arXiv preprint arXiv:1712.03510},
  year   = {2019}
}

Comments

Final version, incorporates referee's comments. Accepted on Advances in Geometry

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

Abstract

Keywords

Cite

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