{"paper":{"title":"Spin Link Homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.RT"],"primary_cat":"math.QA","authors_text":"Ben Elias, David E. V. Rose, Elijah Bodish","submitted_at":"2024-06-28T18:57:10Z","abstract_excerpt":"We put a new spin on Khovanov--Rozansky homology. That is, we equip $\\Lambda^n$-colored $\\mathfrak{sl}_{2n}$ Khovanov--Rozansky homology with an involution whose $\\pm 1$-eigenspaces are link invariants. When $n=1,2,3$ (and assuming technical conjectures for $n \\geq 4$), we prove that this refined invariant categorifies the spin-colored $\\mathfrak{so}_{2n+1}$ quantum link polynomial. Along the way, we partially develop the theory of quantum $\\mathfrak{so}_{2n+1}$ webs and make contact with $\\iota$quantum groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.00189","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/2407.00189/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"}