{"paper":{"title":"On a move reducing the genus of a knot diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Keiichi Sakai, Kenji Daikoku, Masamichi Takase","submitted_at":"2011-11-14T13:50:50Z","abstract_excerpt":"For a knot diagram we introduce an operation which does not increase the genus of the diagram and does not change its representing knot type. We also describe a condition for this operation to certainly decrease the genus. The proof involves the study of a relation between the genus of a virtual knot diagram and the genus of a knotoid diagram, the former of which has been introduced by Stoimenow, Tchernov and Vdovina, and the latter by Turaev recently. Our operation has a simple interpretation in terms of Gauss codes and hence can easily be computer-implemented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3215","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"}