{"paper":{"title":"Khovanov-type homologies of null homologous links in $\\mathbb{RP}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daren Chen","submitted_at":"2021-04-10T14:36:17Z","abstract_excerpt":"Let L be a null homologous link in $\\mathbb{RP}^3$. We define Khovanov-type homologies of L which depend on an extra input $\\alpha = (V_0,V_1,f,g)$ consisting of two graded vectors spaces and two maps between them. With some specific choice of $\\alpha = \\alpha_{APS}$, we recover the categorification of the Kauffman bracket due to Asaeda-Przytycki-Sikora. With another choice of $\\alpha = \\alpha_{HF}$, we construct a spectral sequence from our theory converging to the Heegaard Floer homology of the even branched double cover of $\\mathbb{RP}^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.04779","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/2104.04779/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"}