{"paper":{"title":"Link in $\\mathbb{R}\\mathbb{P}^3$ and the Topological Vertex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.GT","math.MP"],"primary_cat":"math-ph","authors_text":"John Chae","submitted_at":"2025-01-22T01:10:48Z","abstract_excerpt":"We provide the first computations of colored unknots and Hopf link in $\\mathbb{R}\\mathbb{P}^3$ using both the topological vertex and its refinement. Our approach utilizes the toric Calabi-Yau threefold arising from the geometric transition of the cotangent bundle of $\\mathbb{R}\\mathbb{P}^3$ under the large $N$ duality. We find that the link invariants are series in the Kahler parameters of the toric Calabi-Yau manifold and the $q$-expansions of the rational functions of the series have positivity property. We conjecture that they are Poincare series of an infinite dimensional link homology the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.12566","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/2501.12566/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"}