{"paper":{"title":"Topological Complexities of Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ibai Basabe","submitted_at":"2014-02-01T02:31:02Z","abstract_excerpt":"The sphere $S^2$ and the torus $T^2$ are the only closed connected surfaces for which higher topological complexities are known (for each $n\\in\\{2,3,...\\}\\subset\\mathbb{N}$, $\\mathrm{TC}_n(S^2)=n$ and $\\mathrm{TC}_n(T^2)=2n-2$). This text aims to find topological complexities for most other closed connected surfaces. For all but $S^2$, $T^2$, the projective plane ($\\mathbb{R}\\mathbb{P}^2$) and the Klein bottle the $n$-th topological complexity is $2n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0044","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"}