{"paper":{"title":"Complexity of virtual multistrings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"David Freund","submitted_at":"2017-09-05T11:46:24Z","abstract_excerpt":"A virtual $n$-string $\\alpha$ is a collection of $n$ oriented smooth generic loops on a surface $M$. A stabilization of $\\alpha$ is a surgery that results in attaching a handle to $M$ along disks avoiding $\\alpha$, and the inverse operation is a destabilization of $\\alpha$. We consider virtual $n$-strings up to virtual homotopy, i.e., sequences of stabilizations, destabilizations, and homotopies of $\\alpha$.\n  Recently, Cahn proved that any virtual $1$-string can be virtually homotoped to a genus-minimal and crossing-minimal representative by monotonically decreasing both genus and the number "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01340","kind":"arxiv","version":1},"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"}