{"paper":{"title":"Twist families of L-space knots, their genera, and Seifert surgeries","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":"2015-06-15T01:59:25Z","abstract_excerpt":"Conjecturally, there are only finitely many Heegaard Floer L-space knots in $S^3$ of a given genus. We examine this conjecture for twist families of knots $\\{K_n\\}$ obtained by twisting a knot $K$ in $S^3$ along an unknot $c$ in terms of the linking number $\\omega$ between $K$ and $c$. We establish the conjecture in case of $|\\omega| \\neq 1$, prove that $\\{K_n\\}$ contains at most three L-space knots if $\\omega = 0$, and address the case where $|\\omega| = 1$ under an additional hypothesis about Seifert surgeries. To that end, we characterize a twisting circle $c$ for which $\\{ (K_n, r_n) \\}$ co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04455","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"}