{"paper":{"title":"Shadows, ribbon surfaces, and quantum invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alessio Carrega, Bruno Martelli","submitted_at":"2014-04-23T21:00:43Z","abstract_excerpt":"Eisermann has shown that the Jones polynomial of a $n$-component ribbon link $L\\subset S^3$ is divided by the Jones polynomial of the trivial $n$-component link. We improve this theorem by extending its range of application from links in $S^3$ to colored knotted trivalent graphs in $\\#_g(S^2\\times S^1)$, the connected sum of $g\\geqslant 0$ copies of $S^2\\times S^1$.\n  We show in particular that if the Kauffman bracket of a knot in $\\#_g(S^2\\times S^1)$ has a pole in $q=i$ of order $n$, the ribbon genus of the knot is at least $\\frac {n+1}2$. We construct some families of knots in $\\#_g(S^2\\tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5983","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"}