Year: 2025
Type: preprint
Abstract: We identify type-preserving representations $ϕ: π_1(Σ)\to \mathrm{PSL}(2,\mathbb{R})$ of the fundamental group of every punctured surface $Σ= Σ_{g,p}$ that are not Fuchsian yet send all non-peripheral simple closed curves to hyperbolic elements, which give a negative answer to a question of Bowditch. These representations have relative Euler class $e(ϕ) = \pm (χ(Σ) + 1)$, and their $\mathrm{PSL}(2,\mathbb{R})$-conjugacy classes form a full-measure subset of $2p$ connected components of the relative character variety. We further show that, while these representations are not Fuchsian, their restrictions to certain subsurfaces of $Σ$ are Fuchsian.
Source: arXiv (Cornell University)
Author: Ryu, Inyoung
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7106119014
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