{"paper":{"title":"Edge Preserving Maps of the Nonseparating Curve Graphs, Curve Graphs and Rectangle Preserving Maps of the Hatcher-Thurston Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Elmas Irmak","submitted_at":"2017-08-15T22:40:19Z","abstract_excerpt":"Let $R$ be a compact, connected, orientable surface of genus $g$ with $n$ boundary components with $g \\geq 2$, $n \\geq 0$. Let $\\mathcal{N}(R)$ be the nonseparating curve graph, $\\mathcal{C}(R)$ be the curve graph and $\\mathcal{HT}(R)$ be the Hatcher-Thurston graph of $R$. We prove that if $\\lambda : \\mathcal{N}(R) \\rightarrow\\mathcal{N}(R)$ is an edge-preserving map, then $\\lambda$ is induced by a homeomorphism of $R$. We prove that if $\\theta : \\mathcal{C}(R) \\rightarrow \\mathcal{C}(R)$ is an edge-preserving map, then $\\theta$ is induced by a homeomorphism of $R$. We prove that if $R$ is clo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05290","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}