{"paper":{"title":"On a Heegaard Floer theory for tangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.SG"],"primary_cat":"math.GT","authors_text":"Claudius Zibrowius","submitted_at":"2016-10-24T17:01:03Z","abstract_excerpt":"The purpose of this thesis is to define a \"local\" version of Ozsv\\'{a}th and Szab\\'{o}'s Heegaard Floer homology $\\operatorname{\\widehat{HFL}}$ for links in the 3-dimensional sphere, i.e. a Heegaard Floer homology $\\operatorname{\\widehat{HFT}}$ for tangles in the closed 3-ball.\n  After studying basic properties of $\\operatorname{\\widehat{HFT}}$ and its decategorified tangle invariant $\\nabla_T^s$, we prove a glueing theorem in terms of Zarev's bordered sutured Floer homology, which endows $\\operatorname{\\widehat{HFT}}$ with an additional glueing structure. For 4-ended tangles, we repackage thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07494","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"}