{"paper":{"title":"A Categorification of the HOMFLY-PT Polynomial with a Spectral Sequence to Knot Floer Homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Nathan Dowlin","submitted_at":"2017-03-04T06:17:50Z","abstract_excerpt":"Let $E_{k}^{F}(D)$ be the spectral sequence induced by the oriented cube of resolutions on knot Floer homology. We prove that $E_{2}^{F}(D)$ is a triply graded link invariant whose graded Euler characteristic is the HOMFLY-PT polynomial and that the higher pages are link invariants. By construction, the spectral sequence converges to knot Floer homology. We show that the rank of the torsion-free part of $E_{2}^{F}(D)$ is the rank of HOMFLY-PT homology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01401","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":""},"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"}