{"paper":{"title":"Filtered instanton homology and cosmetic surgery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Aliakbar Daemi, Mike Miller Eismeier, Tye Lidman","submitted_at":"2024-10-28T17:46:38Z","abstract_excerpt":"The cosmetic surgery conjecture predicts that for a non-trivial knot in the three-sphere, performing two different Dehn surgeries results in distinct oriented three-manifolds. Hanselman reduced the problem to $\\pm 2$ or $\\pm 1/n$ surgeries being the only possible cosmetic surgeries. We remove the case of $\\pm 1/n$-surgeries using the Chern-Simons filtration on Floer's original irreducible-only instanton homology, reducing the conjecture to the case of $\\pm 2$ surgery on genus $2$ knots with trivial Alexander polynomial. We also prove some similar results for surgeries on knots in $S^2 \\times S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21248","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.21248/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}