{"paper":{"title":"Knot Floer homology and Seifert surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andras Juhasz","submitted_at":"2007-02-17T23:42:05Z","abstract_excerpt":"Let K be a knot in S^3 of genus g and let n>0. We show that if rk HFK(K,g) < 2^{n+1} (where HFK denotes knot Floer homology), in particular if K is an alternating knot such that the leading coefficient a_g of its Alexander polynomial satisfies |a_g| <2^{n+1}, then K has at most n pairwise disjoint non-isotopic genus g Seifert surfaces. For n=1 this implies that K has a unique minimal genus Seifert surface up to isotopy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702514","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"}