{"paper":{"title":"Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Elmas Irmak","submitted_at":"2011-12-07T16:35:10Z","abstract_excerpt":"Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components. Let $\\lambda$ be a simplicial map of the complex of curves, $\\mathcal{C}(N)$, on $N$ which satisfies the following: $[a]$ and $[b]$ are connected by an edge in $\\mathcal{C}(N)$ if and only if $\\lambda([a])$ and $\\lambda([b])$ are connected by an edge in $\\mathcal{C}(N)$ for every pair of vertices $[a], [b]$ in $\\mathcal{C}(N)$. We prove that $\\lambda$ is induced by a homeomorphism of $N$ if $(g, n) \\in \\{(1, 0), (1, 1), (2, 0)$, $(2, 1), (3, 0)\\}$ or $g + n \\geq 5$. Our result implies that superin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1617","kind":"arxiv","version":2},"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"}