Exhaustion of $\mathcal{C}(N)$ via rigid expansions

Jesús Hernández Hernández; Cristhian E. Hidber

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arXiv · 2603.14736

Exhaustion of $\mathcal{C}(N)$ via rigid expansions

Jesús Hernández Hernández·Cristhian E. Hidber

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Abstract

Let $N$ be a connected closed non-orientable surface of genus at least 6. In this work we prove that there exists a finite subgraph $\mathfrak{X}$ (Irmak's finite rigid set from ``Elmas Irmak. Exhausting curve complexes by finite rigid sets on nonorientable surfaces. J.Topol.Anal., 16(2):261--289, 2024'') such that any graph endomorphism $\varphi$ of $\mathcal{C}(N)$ whose restriction to $\mathfrak{X}$ is (locally) injective, $\varphi$ is induced by a homeomorphism of $N$. To prove this, we first prove that $\mathfrak{X}$ and its rigid expansions exhaust $\mathcal{C}(N)$.

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BibTeX RIS

Jesús Hernández Hernández, Cristhian E. Hidber. 2026-03-16. Exhaustion of $\mathcal{C}(N)$ via rigid expansions. https://arxiv.org/abs/2603.14736

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