{"paper":{"title":"Virtual braids and virtual curve diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.QA","authors_text":"Oleg Chterental","submitted_at":"2014-11-23T23:24:35Z","abstract_excerpt":"There is a well known injective homomorphism $\\phi:{\\mathcal {B}}_n \\rightarrow {\\rm Aut}(F_n)$ from the classical braid group ${\\mathcal {B}}_n$ into the automorphism group of the free group $F_n$, first described by Artin. This homomorphism induces an action of ${\\mathcal {B}}_n$ on $F_n$ that can be recovered by considering the braid group as the mapping class group of $H_n$ (an upper half plane with $n$ punctures) acting naturally on the fundamental group of $H_n$.\n  Kauffman introduced virtual links as an extension of the classical notion of a link in ${\\mathbb {R}}^3$. As in the classica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6313","kind":"arxiv","version":4},"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"}