The (non)-relative hyperbolicity of the separating curve graph

2019/10/02 by Jacob Russell, Russell, Jacob, Kate M. Vokes +1
Computer Science · Mathematics · #20F65 (Primary) 57M99 (Secondary) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1910.01051

openalex publication_date 2019/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the separating curve graph of a connected, compact, orientable surface with genus at least 3 and a single boundary component is not relatively hyperbolic. This completes the classification of when the separating curve graph is hyperbolic and relatively hyperbolic initiated by previous works of the authors.

Citations

• On metric relative hyperbolicity

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