{"paper":{"title":"Knot Homology and sheaves on the Hilbert scheme of points on the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.GT","authors_text":"Alexei Oblomkov, Lev Rozansky","submitted_at":"2016-08-10T16:15:11Z","abstract_excerpt":"For each braid $\\beta\\in Br_n$ we construct a $2$-periodic complex $\\mathbb{S}_\\beta$ of quasi-coherent $\\mathbb{C}^*\\times \\mathbb{C}^*$-equivariant sheaves on the non-commutative nested Hilbert scheme $Hilb_{1,n}^{free}$. We show that the triply graded vector space of the hypecohomology $ \\mathbb{H}( \\mathbb{S}_{\\beta}\\otimes \\wedge^\\bullet (\\mathcal{B}))$ with $\\mathcal{B}$ being tautological vector bundle, is an isotopy invariant of the knot obtained by the closure of $\\beta$. We also show that the support of cohomology of the complex $\\mathbb{S}_\\beta$ is supported on the ordinary nested "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03227","kind":"arxiv","version":4},"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"}