{"paper":{"title":"Bordered manifolds with torus boundary and the link surgery formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ian Zemke","submitted_at":"2021-09-23T17:41:52Z","abstract_excerpt":"In this paper, we develop a theory of bordered $\\mathit{HF}^-$ using the link surgery formula of Manolescu and Ozsv\\'{a}th. We interpret their link surgery complexes as type-$D$ modules over an associative algebra $\\mathcal{K}$, which we introduce. We prove a connected sum formula, which we interpret as an $A_\\infty$-tensor product over our algebra $\\mathcal{K}$. Topologically, this connected sum formula may be viewed as a formula for gluing along torus boundary components. We compute several important examples. We show that the dual knot formula of Hedden--Levine and Eftekhary may be interpre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11520","kind":"arxiv","version":6},"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/2109.11520/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"}