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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14736 |
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| _version_ | 1866915865186795520 |
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| author | Hernández, Jesús Hernández Hidber, Cristhian E. |
| author_facet | Hernández, Jesús Hernández Hidber, Cristhian E. |
| contents | 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 $φ$ of $\mathcal{C}(N)$ whose restriction to $\mathfrak{X}$ is (locally) injective, $φ$ is induced by a homeomorphism of $N$. To prove this, we first prove that $\mathfrak{X}$ and its rigid expansions exhaust $\mathcal{C}(N)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14736 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exhaustion of $\mathcal{C}(N)$ via rigid expansions Hernández, Jesús Hernández Hidber, Cristhian E. Geometric Topology 57K20 (Primary) 20F65 (Secondary) 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 $φ$ of $\mathcal{C}(N)$ whose restriction to $\mathfrak{X}$ is (locally) injective, $φ$ is induced by a homeomorphism of $N$. To prove this, we first prove that $\mathfrak{X}$ and its rigid expansions exhaust $\mathcal{C}(N)$. |
| title | Exhaustion of $\mathcal{C}(N)$ via rigid expansions |
| topic | Geometric Topology 57K20 (Primary) 20F65 (Secondary) |
| url | https://arxiv.org/abs/2603.14736 |