{"paper":{"title":"Bounds on alternating surgery slopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Duncan McCoy","submitted_at":"2014-12-02T13:28:56Z","abstract_excerpt":"We show that if $p/q$-surgery on a nontrivial knot $K$ yields the branched double cover of an alternating knot or link, then $|p/q|\\leq 4g(K)+3$. This generalises a bound for lens space surgeries first established by Rasmussen. We also show that all surgery coefficients yielding the double branched cover of an alternating knot or link must be contained in an interval of width two and this full range can be realised only if $K$ is a cable knot. The work of Greene and Gibbons shows that if $S^3_{p/q}(K)$ bounds a sharp 4-manifold $X$, then the intersection form of $X$ takes the form of a changem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0906","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"}