{"paper":{"title":"MICC: A tool for computing short distances in the curve complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kayla Morrell, Matthew Morse, Paul Glenn, William W. Menasco","submitted_at":"2014-08-18T20:00:42Z","abstract_excerpt":"The complex of curves $\\mathcal{C}(S_g)$ of a closed orientable surface of genus $g \\geq 2$ is the simplicial complex having its vertices, $\\mathcal{C}^0(S_g)$, are isotopy classes of essential curves in $S_g$. Two vertices co-bound an edge of the $1$-skeleton, $\\mathcal{C}^1(S_g)$, if there are disjoint representatives in $S_g$. A metric is obtained on $\\mathcal{C}^0(S_g)$ by assigning unit length to each edge of $\\mathcal{C}^1(S_g)$. Thus, the distance between two vertices, $d(v,w)$, corresponds to the length of a geodesic---a shortest edge-path between $v$ and $w$ in $\\mathcal{C}^1 (S_g)$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4134","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"}