Inyoung Ryu

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math.GT2026

From Bowditch question to Goldman conjecture for type-preserving representations

Viraj Joshi, Inyoung Ryu

For punctured surfaces $Σ_{g, p}$ of genus $g ⩾ 2$ , we explore the dynamics of the mapping class group action on the relative $PSL (2, R)$ -character varieties…

math.GT2025

On totally hyperbolic non-Fuchsian type-preserving representations

Inyoung Ryu

We identify type-preserving representations $ϕ : π_{1} (Σ) \to PSL (2, R)$ of the fundamental group of every punctured surface $Σ = Σ_{g, p}$ that are not Fuchsian yet sen…

math.GT2025

Connected components of the space of type-preserving representations

Inyoung Ryu, Tian Yang

We complete the characterization of the connected components of the space of type-preserving representations of a punctured surface group into $PSL (2, R)$ . We show…