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<p>Let <i>N</i> be a connected finite type nonorientable surface with or without boundary components and punctures. We prove that the graph of nonseparating curves of <i>N</i> is connected and Gromov hyperbolic with a constant which does not depend on the topological type of the surface by using the bicorn curves introduced by Przytycki and Sisto. The proof is based on the argument by Rasmussen on the uniform hyperbolicity of graphs of nonseparating curves for finite type orientable surfaces.</p>

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Uniform hyperbolicity of nonseparating curve graphs of nonorientable surfaces

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Erika Kuno

摘要

Let N be a connected finite type nonorientable surface with or without boundary components and punctures. We prove that the graph of nonseparating curves of N is connected and Gromov hyperbolic with a constant which does not depend on the topological type of the surface by using the bicorn curves introduced by Przytycki and Sisto. The proof is based on the argument by Rasmussen on the uniform hyperbolicity of graphs of nonseparating curves for finite type orientable surfaces.