{"paper":{"title":"Homological Link Invariants from Floer Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.QA","math.RT","math.SG"],"primary_cat":"hep-th","authors_text":"Elise LePage, Mina Aganagic, Miroslav Rapcak","submitted_at":"2023-05-22T20:44:43Z","abstract_excerpt":"There is a generalization of Heegaard-Floer theory from ${\\mathfrak{gl}}_{1|1}$ to other Lie (super)algebras $^L{\\mathfrak{g}}$. The corresponding category of A-branes is solvable explicitly and categorifies quantum $U_q(^L{\\mathfrak{g}})$ link invariants. The theory was discovered in \\cite{A1,A2}, using homological mirror symmetry. It has novel features, including equivariance and, if $^L{\\mathfrak{g}} \\neq {\\mathfrak{gl}}_{1|1}$, coefficients in categories. In this paper, we describe the theory and how it is solved in detail in the two simplest cases: the ${\\mathfrak{gl}}_{1|1}$ theory itsel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.13480","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/2305.13480/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"}