{"paper":{"title":"Virtual Seifert Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Micah Chrisman","submitted_at":"2017-12-15T15:33:41Z","abstract_excerpt":"A virtual knot that has a homologically trivial representative $\\mathscr{K}$ in a thickened surface $\\Sigma \\times [0,1]$ is said to be an almost classical (AC) knot. $\\mathscr{K}$ then bounds a Seifert surface $F\\subset \\Sigma \\times [0,1]$. Seifert surfaces of AC knots are useful for computing concordance invariants and slice obstructions. However, Seifert surfaces in $\\Sigma \\times [0,1]$ are difficult to construct. Here we introduce virtual Seifert surfaces of AC knots. These are planar figures representing $F \\subset \\Sigma \\times [0,1]$. An algorithm for constructing a virtual Seifert su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05715","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"}