{"paper":{"title":"Knot surgery formulae for instanton Floer homology I: the main theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Fan Ye, Zhenkun Li","submitted_at":"2022-06-21T02:09:37Z","abstract_excerpt":"We prove an integral surgery formula for framed instanton homology $I^\\sharp(Y_m(K))$ for any knot $K$ in a $3$-manifold $Y$ with $[K]=0\\in H_1(Y;\\mathbb{Q})$ and $m\\neq 0$. Though the statement is similar to Ozsv\\'ath-Szab\\'o's integral surgery formula for Heegaard Floer homology, the proof is new and based on sutured instanton homology $SHI$ and the octahedral lemma in the derived category. As a corollary, we obtain an exact triangle between $I^\\sharp(Y_m(K))$, $I^\\sharp(Y_{m+k}(K))$ and $k$ copies of $I^\\sharp(Y)$ for any $m\\neq 0$ and large $k$. In the proof of the formula, we discover man"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.10077","kind":"arxiv","version":3},"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/2206.10077/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"}