{"paper":{"title":"Seifert vs slice genera of knots in twist families and a characterization of braid axes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kenneth L. Baker, Kimihiko Motegi","submitted_at":"2017-05-29T19:40:50Z","abstract_excerpt":"Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\\{K_n\\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) < C$ for some constant $C$ for infinitely many integers $n > 0$ or $g(K_n) / g_4(K_n) \\to 1$ as $n \\to \\infty$, then either the winding number of $K$ about $c$ is zero or the winding number equals the wrapping number. As a key application, if $\\{K_n\\}$ or the mirror twist family $\\{\\overline{K_n}\\}$ contains infinitely many tight fiber"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10373","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"}