{"paper":{"title":"Untangling two systems of noncrossing curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Eric Sedgwick, Ji\\v{r}\\'i Matou\\v{s}ek, Martin Tancer, Uli Wagner","submitted_at":"2013-02-26T16:10:10Z","abstract_excerpt":"We consider two systems of curves $(\\alpha_1,...,\\alpha_m)$ and $(\\beta_1,...,\\beta_n)$ drawn on a compact two-dimensional surface $M$ with boundary.\n  Each $\\alpha_i$ and each $\\beta_j$ is either an arc meeting the boundary of $M$ at its two endpoints, or a closed curve. The $\\alpha_i$ are pairwise disjoint except for possibly sharing endpoints, and similarly for the $\\beta_j$. We want to \"untangle\" the $\\beta_j$ from the $\\alpha_i$ by a self-homeomorphism of $M$; more precisely, we seek a homeomorphism $\\phi:M\\rightarrow M$ fixing the boundary of $M$ pointwise such that the total number of c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6475","kind":"arxiv","version":5},"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"}