Geometrization of purely hyperbolic representations in PSL₂\Bbb R

2017/12/10 by Faraco, Gianluca
#57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1712.03510

Abstract

Let S be a surface of genus g at least 2. A representation ρ:π₁S\longrightarrow PSL₂\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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