{"paper":{"title":"Concordance invariants of doubled knots and blowing up","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kwan Yong Lee, Se-Goo Kim","submitted_at":"2017-12-10T08:26:59Z","abstract_excerpt":"Let $\\nu$ be either the Ozsv\\'ath-Szab\\'o $\\tau$-invariant or the Rasmussen $s$-invariant, suitably normalized. For a knot $K$, Livingston and Naik defined the invariant $t_\\nu(K)$ to be the minimum of $k$ for which $\\nu$ of the $k$-twisted positive Whitehead double of $K$ vanishes. They proved that $t_\\nu(K)$ is bounded above by $-TB(-K)$, where $TB$ is the maximal Thurston-Bennequin number. We use a blowing up process to find a crossing change formula and a new upper bound for $t_\\nu$ in terms of the unknotting number. As an application, we present infinitely many knots $K$ such that the dif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03486","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"}