{"paper":{"title":"Fiber detection for state surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"David Futer","submitted_at":"2012-01-08T17:37:28Z","abstract_excerpt":"Every Kauffman state \\sigma of a link diagram D(K) naturally defines a state surface S_\\sigma whose boundary is K. For a homogeneous state \\sigma, we show that K is a fibered link with fiber surface S_\\sigma if and only if an associated graph G'_\\sigma is a tree. As a corollary, it follows that for an adequate knot or link, the second and next-to-last coefficients of the Jones polynomial are obstructions to certain state surfaces being fibers for K.\n  This provides a dramatically simpler proof of a theorem from [arXiv:1108.3370]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1643","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"}