{"paper":{"title":"A general Heegaard Floer surgery formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ian Zemke","submitted_at":"2023-08-29T22:40:29Z","abstract_excerpt":"We give several new perspectives on the Heegaard Floer Dehn surgery formulas of Manolescu, Ozsv\\'{a}th and Szab\\'{o}. Our main result is a new exact triangle in the Fukaya category of the torus which gives a new proof of these formulas. This exact triangle is different from the one which appeared in Ozsv\\'{a}th and Szab\\'{o}'s original proof. This exact triangle simplifies a number of technical aspects in their proofs and also allows us to prove several new results. A first application is an extensions of the link surgery formula to arbitrary links in closed 3-manifolds, with no restrictions o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.15658","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.15658/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"}