{"paper":{"title":"Knot Categorification from Mirror Symmetry, Part II: Lagrangians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.RT","math.SG"],"primary_cat":"hep-th","authors_text":"Mina Aganagic","submitted_at":"2021-05-13T01:55:12Z","abstract_excerpt":"I provide two solutions to the problem of categorifying quantum link invariants, which work uniformly for all gauge groups and originate in geometry and string theory. The first is based on a category of equivariant B-type branes on ${\\cal X}$ which is a moduli space of singular $G$-monopoles on ${\\mathbb R}^3$. In this paper, I give the second approach, which is based on a category of equivariant A-type branes on $Y$ with potential $W$. The first and the second approaches are related by equivariant homological mirror symmetry: $Y$ is homological mirror to $X$, a core locus of ${\\cal X}$ prese"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.06039","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.06039/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"}