{"paper":{"title":"Minimizing intersection points of curves under virtual homotopy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"David Freund, Rustam Sadykov, Vladimir Chernov","submitted_at":"2017-08-10T03:44:26Z","abstract_excerpt":"A flat virtual link is a finite collection of oriented closed curves $\\mathfrak L$ on an oriented surface $M$ considered up to virtual homotopy, i.e., a composition of elementary stabilizations, destabilizations, and homotopies. Specializing to a pair of curves $(L_1,L_2)$, we show that the minimal number of intersection points of curves in the virtual homotopy class of $(L_1, L_2)$ equals to the number of terms of a generalization of the Anderson--Mattes--Reshetikhin Poisson bracket. Furthermore, considering a single curve, we show that the minimal number of self-intersections of a curve in i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03064","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"}